CBSE Class 9 Answered
Q-9
If a+c+c=5 and ab+bc+ca=15, find the value of
Asked by kishor.kp14 | 18 Jun, 2019, 10:07: AM
Expert Answer
(a + b)3 + (b + c)3 + (c + a)3 - 3(a + b)(b +c)(c + a) = 2a3 + 2b3 +2c3 - 6abc
2a3 + 2b3 + 2c3 - 6abc = 2(a3 + b3 +c3 - 3abc) = 2(a + b+ c)[a2 + b2 +c2 - (ab +bc + ca)] -------- (I)
(a + b + c)2 = a2 +b2 +c2 + 2(ab +bc + ca)
52 = a2 +b2 + c2 + 30
25 - 30 = a2 + b2 + c2
- 5 = a2 +b2 + c2
Put the values in equation (I) we get
(a + b)3 + (b + c)3 + (c + a)3 - 3(a + b)(b +c)(c + a) = 2(a + b+ c)[a2 + b2 +c2 - (ab +bc + ca)]
2a3 + 2b3 + 2c3 - 6abc = 2(a3 + b3 +c3 - 3abc) = 2(a + b+ c)[a2 + b2 +c2 - (ab +bc + ca)] -------- (I)
(a + b + c)2 = a2 +b2 +c2 + 2(ab +bc + ca)
52 = a2 +b2 + c2 + 30
25 - 30 = a2 + b2 + c2
- 5 = a2 +b2 + c2
Put the values in equation (I) we get
(a + b)3 + (b + c)3 + (c + a)3 - 3(a + b)(b +c)(c + a) = 2(a + b+ c)[a2 + b2 +c2 - (ab +bc + ca)]
= 2(5)(-5 - 15)
= 2(5)(-20) = - 200
Answered by Sneha shidid | 18 Jun, 2019, 10:28: AM
Concept Videos
-
Algebraic Identities: Cubic Type
Listing of algebraic identities for cubic Polynomials and simplify the comp... -
Algebraic identities for cubic Polynomials
Listing of algebraic identities for cubic Polynomials and simplify the comp... -
Algebraic Identities: Cubic Type
This video lists the algebraic identities for cubic Polynomials and simplif...
CBSE 9 - Maths
Asked by durgavenkatlakshmi1 | 20 Mar, 2024, 03:56: PM
ANSWERED BY EXPERTCBSE 9 - Maths
Asked by shivalaxmi0205 | 23 Feb, 2023, 10:28: PM
ANSWERED BY EXPERTCBSE 9 - Maths
Asked by shivalaxmi0205 | 21 Feb, 2023, 07:34: PM
ANSWERED BY EXPERTCBSE 9 - Maths
Asked by shivalaxmi0205 | 21 Feb, 2023, 07:33: PM
ANSWERED BY EXPERTCBSE 9 - Maths
Asked by mmansingh949 | 21 Jun, 2022, 09:54: AM
ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by dalalvansh4 | 02 Jun, 2022, 07:03: PM
ANSWERED BY EXPERTCBSE 9 - Maths
Asked by s1044kasturipriyambada026582 | 27 May, 2022, 12:02: PM
ANSWERED BY EXPERTCBSE 9 - Maths
Asked by abilash8b | 06 Jan, 2022, 12:27: PM
ANSWERED BY EXPERT
