Question

The difference of squares of two natural number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.

Answer 1

SOLUTION :  

Given : Difference of squares of two natural number is 88 & larger number is 5 less than twice the smaller number.

Let x be the smaller number & larger number be 2x - 5

A.T.Q

(2x - 5)² - x² = 88

[(2x)² + 5² - 2 × 2x × 5 ] - x² = 88

4x² + 25 - 20x - x² = 88

4x² - x² - 20x + 25 - 88 = 0

3x² - 20x - 63 = 0

3x² - 27x + 7x - 63 = 0

[By middle term splitting]

3x(x - 9) + 7(x - 9) = 0

(x - 9) (3x + 7) = 0

(x - 9)  = 0  or  (3x + 7) = 0

x = 9 or 3x = - 7

x = 9 or x = - 7/3

Since, x is a natural number, so x ≠ - 7/3  

Therefore, x = 9  

Smaller number = x = 9 , then larger number = 2x - 5 = 2(9) - 5 = 18 - 5 = 13

Hence, the two numbers are 9 and 13 .

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

łєт тнє sмαłłєя ησ: вє x
тнєη тнє łαяgєя ησ: ıs 2x - 5

gıѵєη ,

(2x - 5)² - x² = 88

4x² -20x + 25 - x² = 88

3x² - 20x - 63 = 0

3x² - 27x + 7x - 63

3x(x - 9) + 7(x - 9)

(3x + 7) (x - 9)

x = -7/3 . x = 9

тнє ѵαłυє cαηησт вє ηєgαтıѵє , нєηcє , x = 9 ıs тнє cσяяєcт ѵαłυє.

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2x - 5 = 18 - 5 = 13
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тнє ησ:s αяє 9 αη∂ 13