Question

given X + Y is equal to 15 and X Y is equal to 54 find the value of x square minus y square

Answer 1

Answer:

±45

Step-by-step explanation:

x + y = 15

x^2 + y^2 + 2xy = 225   [ squaring both sides ]

given, xy = 54

SO x^2 + y^2 - 2xy = 225 - 4xy = 225 - 216 = 9

(x - y)^2 = (±3)^2  => x - y = ±3

So, x^2 - y^2 = (x + y)(x - y) = 15*(±3) = ±45

Both ± values come because if x > y, then the value is +ve and if x < y, then value is -ve.

Answer 2

X+Y=15 , XY=54

X^2 - Y^2 = (X-Y) (X+Y)

(X-Y)^2 = X^2 + Y^2 - 2XY =  X^2+Y^2 + 2XY - 4XY

(X+Y)^2 - 4XY

(15)^2 - 4*54

225-216=9

X-Y= root 9=+- root 3

X^2-Y^2=3*15=45 if X-Y=+3

-3*15=45 if X-Y = -3