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.
please give answer with full explanation. no irrelevant answers.
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20
Step-by-step explanation:
Let the smaller and larger of two parts be x and y. According to question,
y2 = 18x
Sum of the squares of the two parts is 208.
x2 + y2 = 208
x2 + 18x - 208 = 0
x2 + 26x - 8x + 208 = 0
x(x + 26) - 8(x + 26) = 0
(x-8)(x + 26) = 0
x = 8 or x = -26 (rejected as part of pice never be negative)
y = √18x
=√18 x 8
= √144
= 12
Hence, the no. is 8 + 12 = 20
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