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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

ConceptSolutions of Quadratic Equations by Factorization

#### 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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