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Mathematics

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.

Quadratic Equations

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Answer

Let smaller part be x.

According to second part of question,

Larger part = 8x\sqrt{8x}

According to first part of question,

x2 + (8x)2(\sqrt{8x})^2 = 20

x2 + 8x = 20

x2 + 8x - 20 = 0

x2 + 10x - 2x - 20 = 0

x(x + 10) - 2(x + 10) = 0

(x - 2)(x + 10) = 0

x - 2 = 0 or x + 10 = 0

x = 2 or x = -10.

Since number is positive,

∴ x ≠ -10

Larger part = 8x=8(2)=16=4.\sqrt{8x} = \sqrt{8(2)} = \sqrt{16} = 4.

Number = Smaller part + Larger part = 2 + 4 = 6.

Hence, number = 6.

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