If a(x+y) = b(x-y) = 2ab,then the value of 2( | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given: $a(x+y) = 2ab$ and $b(x-y) = 2ab$.From $a(x+y) = 2ab$,we get $x+y = 2b$  $(i)$.From $b(x-y) = 2ab$,we get $x-y = 2a$  $(ii)$.Adding $(i)$ a

Vedclass · Accepted Answer

$4(a^2 + b^2)$

Vedclass · Answer

(D) Given: $a(x+y) = 2ab$ and $b(x-y) = 2ab$.From $a(x+y) = 2ab$,we get $x+y = 2b$  $(i)$.From $b(x-y) = 2ab$,we get $x-y = 2a$  $(ii)$.Adding $(i)$ and $(ii)$:$(x+y) + (x-y) = 2b + 2a$$2x = 2(a+b) \implies x = a+b$.Subtracting $(ii)$ from $(i)$:$(x+y) - (x-y) = 2b - 2a$$2y = 2(b-a) \implies y = b-a$.Now,calculate $2(x^2 + y^2)$:$2((a+b)^2 + (b-a)^2)$$= 2(a^2 + b^2 + 2ab + b^2 + a^2 - 2ab)$$= 2(2a^2 + 2b^2)$$= 4(a^2 + b^2)$.

If $a(x+y) = b(x-y) = 2ab$,then the value of $2(x^2 + y^2)$ is:

Similar Questions

The condition that one root of the equation $ax^2 + bx + c = 0$ is three times the other is

$I. x^{2}+10 x+24=0$
$II. 4 y^{2}-17 y+18=0$

If $x+y=3$ and $xy=2$,then find the value of $x^3-y^3$.

$x=3$ is a solution of the equation $3x^{2} + (k-1)x + 9 = 0$ if $k$ has the value:

Solve the given two equations and select the correct option.
$I.$ $676 x^{2}-1=0$
$II.$ $y=\frac{1}{\sqrt[3]{13824}}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module