If x-2 y=3 and x y=5, find the value of x^{2}-4 y^{2}.

SSC CHSL 12 Oct 2020 Shift 1 Paper

Question : 74 of 100

Marks: +1, -0

x-2 y=3

and

x y=5

, find the value of

x^{2}-4 y^{2}

Solution:

x-2 y=3

(squaring on both sides)

x^{2}+4 y^{2}-4 x y=9

x^{2}+4 y^{2}-4 x y+4 x y-4 x y=9

(x+2 y)^{2}-8 x y=9

(\ ∵x y=5)

(x+2 y)^{2}-8 \×5=9

(x+2 y)^{2}=49

x+2 y=7

Now,

x^{2}-4 y^{2}=(x+2 y)(x-2 y)

[\ ∵a^{2}-b^{2}=(a+b)(a-b)]

=7 \×3=21

Go to Question:

Prev Question

Next Question