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Question

The difference of the squares of two positive integers is 180. The square of the smaller number is 8 times the larger, find the numbers.


Solution

Let the larger number be x.

Then according to the question,

Square of the smaller number = 8x, then

x2-8x=180x2-8x-180=0x2-18x+10x-180=0x(x-18)+10(x-18)=0(x+10)(x-18)=0x+10=0 or x-18=0x=-10 or x=18

Since, being a positive integer so, x cannot be negative,

Therefore, larger number = 18.

then the smaller number = 8×18=12

Thus, the two positive numbers are 12 and 18.


Mathematics
RD Sharma (2016)
Standard X

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