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The Sum of the Squares of Two Numbers as 233 and One of the Numbers as 3 Less than Twice the Other Number Find the Numbers. - CBSE Class 10 - Mathematics

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Question

The sum of the squares of two numbers as 233 and one of the numbers as 3 less than twice the other number find the numbers.

Solution

Let the numbers be integers. One of the numbers be x. So, the other will be (2x - 3).

Then according to question,

x2 + (2x - 3)2 = 233

x2 + 4x2 - 12x + 9 = 233

5x2 - 12x + 9 - 233 = 0

5x2 - 12x - 224 = 0

5x2 - 40x + 28x - 224 = 0

5x(x - 8) + 28(x - 8) = 0

(x - 8)(5x + 28) = 0

x - 8 = 0

x = 8

Or

5x + 28 = 0

5x = -28

x = -28/5

Since, we have assumed the numbers to be integers, so x cannot be a rational number/fraction.

Therefore, for x = 8

Other number = (2x - 3) = 2(8) - 3 = 16 - 3 = 13

Thus, whole numbers be 8, 13.

  Is there an error in this question or solution?

APPEARS IN

Solution The Sum of the Squares of Two Numbers as 233 and One of the Numbers as 3 Less than Twice the Other Number Find the Numbers. Concept: Solutions of Quadratic Equations by Factorization.
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