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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 P - ICSE Class 10 - Mathematics

Question

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.

Solution

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

smallerpart  = 2

larger part =  sqrt(8 xx 2) = 4

Thus, the required number = 2 +  4 = 6

Is there an error in this question or solution?

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Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6A | Q: 17
2009-2010 (March) (with solutions)
Question 10.1 | 4.00 marks

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Solution 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 P Concept: Quadratic Equations.
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