Question 71

If $$X^2 + Y^2= 100$$ and $$X : Y = 4 : 3$$, then what is the value of $$X^2 - Y^2$$?

Solution

let X:Y= 4a:3a

$$X^2 + Y^2= 100$$

Now put x, y value in above equation

$$(4a)^2 + (3a)^2= 100$$

$$25a^2 = 100$$

a = 2

X= 8

Y= 6

$$X^2 - Y^2$$ = $$8^2 - 6^2 $$ = 64 - 36 = 28

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