Question

find the value of the following by using: (x+y) (x-y) = x²-y²
a) (5x-4) (5x+4)
b) (x-2) (x-2)​

Answer 1

Step-by-step explanation:

X/Y = 3/2 So X = 3Y/2

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

Now replace the X value from first equation

= [ (3Y/2)^2 + Y^2] / [ ((3Y/2)^2 - Y^2]

= [ (9Y^2/4) + Y^2] / [ (9Y^2/4) - Y^2]

= [ (9Y^2 + 4Y^2)/4] / [ (9Y^2 - 4Y^2)/4]

= (9Y^2 + 4Y^2) / (9Y^2 - 4Y^2)

= 13Y^2 / 5Y^2

= 13/5

If you have to solve this in any competition exam then just simply replace any value in X & Y which satisfy the equation X/Y = 3/2.

Example: X = 3 & Y = 2 and X and Y should not equal to 0.

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

= 3^2 + 2^2 / 3^2 - 2^2

= 9 + 4 / 9 - 4

= 13/5

This will save more time. I hope you understand.