Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 9 Answered

If X=[(a+2b)^1/2+(a-2b)^1/2] / [(a+2b)^1/2-(a-2b)^1/2] then prove (b^2*x^2)-abx+b^2=0
 
Asked by abinash.gupta003 | 24 Jul, 2016, 02:30: PM
answered-by-expert Expert Answer
begin mathsize 12px style Given space straight x equals fraction numerator square root of straight a plus 2 straight b end root plus square root of straight a minus 2 straight b end root over denominator square root of straight a plus 2 straight b end root minus square root of straight a minus 2 straight b end root end fraction Rationalise space the space denominator straight x equals fraction numerator left parenthesis square root of straight a plus 2 straight b end root plus square root of straight a minus 2 straight b end root right parenthesis left parenthesis square root of straight a plus 2 straight b end root plus square root of straight a minus 2 straight b end root right parenthesis over denominator left parenthesis square root of straight a plus 2 straight b end root minus square root of straight a minus 2 straight b end root right parenthesis left parenthesis square root of straight a plus 2 straight b end root plus square root of straight a minus 2 straight b end root right parenthesis end fraction rightwards double arrow straight x equals fraction numerator left parenthesis square root of straight a plus 2 straight b end root plus square root of straight a minus 2 straight b end root right parenthesis squared over denominator straight a plus 2 straight b minus straight a plus 2 straight b end fraction rightwards double arrow straight x equals fraction numerator straight a plus 2 straight b plus straight a minus 2 straight b plus 2 square root of straight a plus 2 straight b end root square root of straight a minus 2 straight b end root over denominator 4 straight b end fraction rightwards double arrow straight x equals fraction numerator 2 straight a plus 2 square root of straight a plus 2 straight b end root square root of straight a minus 2 straight b end root over denominator 4 straight b end fraction rightwards double arrow straight x equals fraction numerator straight a plus square root of straight a plus 2 straight b end root square root of straight a minus 2 straight b end root over denominator 2 straight b end fraction rightwards double arrow 2 bx equals straight a plus square root of straight a plus 2 straight b end root square root of straight a minus 2 straight b end root rightwards double arrow 2 bx minus straight a equals square root of straight a plus 2 straight b end root square root of straight a minus 2 straight b end root Squaring space both space sides rightwards double arrow left parenthesis 2 bx minus straight a right parenthesis squared equals left parenthesis square root of straight a plus 2 straight b end root square root of straight a minus 2 straight b end root right parenthesis squared rightwards double arrow 4 straight b squared straight x squared plus straight a squared minus 4 abx equals left parenthesis straight a plus 2 straight b right parenthesis left parenthesis straight a minus 2 straight b right parenthesis rightwards double arrow 4 straight b squared straight x squared plus straight a squared minus 4 abx equals straight a squared minus 4 straight b squared rightwards double arrow 4 straight b squared straight x squared minus 4 abx equals negative 4 straight b squared rightwards double arrow 4 straight b squared straight x squared minus 4 abx plus 4 straight b squared equals 0 rightwards double arrow straight b squared straight x squared minus abx plus straight b squared equals 0 Hence space proved. end style
Answered by Rebecca Fernandes | 25 Jul, 2016, 09:35: AM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 9 - Maths
13. If x = (2 + sqrt(3)) find the value of x ^ 2 + 1/(x ^ 2)
Asked by monika.vns14 | 18 Apr, 2024, 05:15: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
3√5+√3/√5-√3
Asked by gulshanelectronics2017 | 15 Apr, 2024, 05:35: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
how to solve it
question image
Asked by singhanjali0199 | 12 Apr, 2024, 08:29: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
locate √2 on number line
Asked by rathoreraj7296 | 31 Mar, 2024, 08:09: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Rationalize the denomination of √3+√2 /√3-√2
Asked by gurucharansingh19975 | 23 Feb, 2024, 09:28: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
i can't understand this ques
question image
Asked by satorugoku369 | 22 Feb, 2024, 08:56: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
2+√3÷2-√3 - 2-√3÷2-√3
Asked by seebasajan1 | 11 Jan, 2024, 06:33: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
what is whole number
Asked by omt7989 | 02 Jan, 2024, 07:48: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
find five rational number between 3/7 and 2/ 5
Asked by lalitayadav7891 | 06 Dec, 2023, 07:30: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
If a + b x √3 equals to 2 into root 3 minus 2 upon 2 root 3 + 2 find values of a and b
Asked by singha83147 | 04 Oct, 2023, 09:28: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×