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The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

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3 months ago Anand Kumar Pandey
3071 Points
```							Dear StudentLet us say, the larger and smaller number bexandyrespectively. As per the question given,x^2-y^2= 180andy^2= 8x⇒x^2- 8x= 180⇒x^2- 8x- 180 = 0⇒x^2- 18x+ 10x- 180 = 0⇒x(x- 18) +10(x- 18) = 0⇒(x- 18)(x+ 10) = 0⇒x= 18, -10However, the larger number cannot considered as negative number, as 8 times of the larger number will be negative and hence, the square of the smaller number will be negative which is not possible.Therefore, the larger number will be 18 only.x= 18∴y^2= 8x = 8 × 18 = 144⇒y= ±√144 = ±12∴Smaller number = ±12Therefore, the numbers are 18 and 12 or 18 and -12.Thanks
```
3 months ago
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