A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the numebr.

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Solution

Given smaller part = x

(larger part)² = 8x

sum of the squares of the two parts = 20
8x+ x²= 20
x² +8x-20=0
⇒x² +10x-2x-20=0
⇒x(x+10) -2(x+10)=0
⇒(x+10)(x-2)=0
∴x+10=0 or x-2 =0
x= -10 or x=2
we take positive value

i) the required numbers
x= 2
larger number =√8x
= √8*2
= √16
= 4

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A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.

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