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Question

The difference of square of two no. Is 180. The square of the smaller no. Is 8 times the larger no. Find the two no.


Solution

Let X & Y be he two numbers  & X>Y

by quwstion,  X^2 -Y^2 = 180  ....eq.1)
&  Y^2 = 8X

putting value of Y^2 in eq1)

X^2-8X=180
or X^2 -8X -180 = 0
or X^2 - 18X+10X-180=0
or X(X-18) + 10(X-18) = 0
or (X-18)(X+10) =0
or X=18 or -10

therefore, Y^2 = 8X = 8*18 = 144 or Y=12
if X=-10, then Y^2= -80, & Y is meaningless

Hence X=18

Ans. the nos. are 18 & 12

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