Yesterday i was doing this question but it is very tough so i want to simple solution of this question please describe me the best solution of this question 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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# 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. Q.7

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Let us say, the larger and smaller number beÂ

xÂ andÂy,Â respectively.As per the question given,

x^{2Â }â€“Ây^{2}Â = 180 andÂy^{2}Â = 8xâ‡’Â

x^{2Â }â€“ 8xÂ = 180â‡’Â

x^{2Â }â€“Â 8xÂ â€“ 180 = 0â‡’Â

x^{2Â }â€“ 18xÂ + 10xÂ â€“ 180 = 0â‡’Â

x(xÂ â€“ 18)Â +10(xÂ â€“ 18) = 0â‡’ (

xÂ â€“ 18)(xÂ + 10) = 0â‡’Â

xÂ = 18, -10However, the larger number cannot be 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.

xÂ = 18âˆ´Â

y^{2}Â = 8x = 8 Ã— 18 = 144â‡’Â

yÂ = Â±âˆš144Â = Â±12âˆ´ Smaller number = Â±12

Therefore, the numbers are 18 and 12 or 18 and -12.

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