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ICSE Class 10 Answered

if  x=fraction numerator square root of a plus 3 b end root plus square root of a minus 3 b end root over denominator square root of a plus 3 b end root minus square root of a minus 3 b end root end fraction, prove that: 3 b x to the power of 2 space end exponent minus 2 a x plus 3 b equals 0
Asked by fenny.gajjar | 06 Mar, 2019, 11:06: PM
answered-by-expert Expert Answer
begin mathsize 12px style x space equals space fraction numerator square root of a plus 3 b end root space plus space square root of a space minus space 3 b end root over denominator square root of a plus 3 b end root space minus space square root of a space minus space 3 b end root end fraction
x space equals space fraction numerator square root of a plus 3 b end root space plus space square root of a space minus space 3 b end root over denominator square root of a plus 3 b end root space minus space square root of a space minus space 3 b end root end fraction space space cross times fraction numerator square root of a plus 3 b end root space plus space square root of a space minus space 3 b end root over denominator square root of a plus 3 b end root space plus space square root of a space minus space 3 b end root end fraction equals space fraction numerator a space plus 3 b space plus a space minus 3 b space plus 2 square root of a squared minus 9 b squared end root over denominator 6 b end fraction
x space equals space fraction numerator a plus square root of a squared minus 9 b squared end root over denominator 3 b end fraction space space space............. left parenthesis 1 right parenthesis
x squared space equals space open parentheses fraction numerator a plus square root of a squared minus 9 b squared end root over denominator 3 b end fraction close parentheses squared space equals space fraction numerator 1 over denominator 9 b squared end fraction open square brackets 2 a squared space minus 9 b squared space plus space 2 a square root of a squared minus 9 b squared end root close square brackets space space............. left parenthesis 2 right parenthesis
end style
by substituting x and x2 using eqn.(1) and eqn.(2) , we can prove,  3b x2 -2ax + 3b = 0
Answered by Thiyagarajan K | 07 Mar, 2019, 12:03: AM
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