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प्रश्न
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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उत्तर
Let the smaller part be x
Then, (larger part)2 = 8x
∴ Larger part = `sqrt(8x)`
Now, the sum of the squares of both the terms is given to be 20
`x^2 + (sqrt(8x))^2 = 20`
`⇒ x^2 + 8x = 20`
`=> x^2 + 8x - 20 = 0`
`=> x^2 - 2x + 10x - 20 = 0`
`=> x(x - 2) + 10(x - 2) = 0`
`=> (x - 2)(x + 10) = 0`
`=> x = 2 or x = -10`
x = –10 is rejected as it is negative
∴ x = 2
Smaller part = 2
Larger part = `sqrt(8 xx 2)` = 4
Thus, the required number = 2 + 4 = 6
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