Question

If x + y = 3 and x – y = 5, then x2 – y2 = A. 4 B. 8 C. 15 D. 16 E. 64?

Answer 1

Step-by-step explanation:

x + y = 3

x - y = 5

-----------------

2x = 8 add together

x = 4

y = -1

x^2 - y^2 = 16 - 1 = 15.

Answer = C.

Alternative way

(x+y) (x -y) = x^2 + xy - xy - y^2 = x^2 - y^2.

Hence,

3 * 5 = 15.

Answer = C

Answer 2

$Given \: x + y = 3 \: --(1)$

$and \: x - y = 5 \: ---(2)$

/* Multiplying equations (1) and (2) , we get */

$\implies ( x + y )( x - y ) = 3 \times 5$

$\implies x^{2} - y^{2} = 15 \: --(3)$

$Compare \: equation \: (3) \: with$

$\: x^{2} - y^{2} = A , we \:get$

$\implies A = 15$

Therefore.,

$Option \: \pink { ( C ) } \:is \: correct.$

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