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The Sum of the Square of Two Numbers is 233. If One of the Numbers is 3 Less than Twice the Other Number. Find the Numbers. - Mathematics

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प्रश्न

The sum of the square of two numbers is 233. If one of the numbers is 3 less than twice the other number. Find the numbers.

बेरीज
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उत्तर

Let the numbers be x, 2x - 3. Then, 

x2 + (2x-3)2 = 233 

⇒ x2 + 4x2 + 9 - 12x = 233 

⇒ 5 x2 -12x - 224 = 0 

⇒ 5 x2 - 40x + 28x - 224 = 0 

⇒ 5x (x - 8) + 28(x - 8) = 0 

⇒ (5x + 28)(x - 8) = 0 

⇒ x = 8  (As the number have to be natural number) 

⇒ Other number = 2 x 8 - 3 =13 

Hence, the numbers are 8 and 13 

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पाठ 7: Problems Based On Quadratic Equations - Exercise 7.1

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फ्रँक Mathematics - Part 2 [English] Class 10 ICSE
पाठ 7 Problems Based On Quadratic Equations
Exercise 7.1 | Q 13

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