# The difference of the square of two numbers is 88. If one number is 5 less than twice the other,find the two numbers.

2
by deeenbe

2015-03-25T08:38:25+05:30

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Let smaller number= x & larger number= y
According to given condition,
y^2 - x^2 = 88 ..........(1)
y = 2x - 5  ...............(2)
Put value of y frm equation 2 in eq 1
(2x-5)^2 - x^2 = 88
⇒ 4x^2 - 20x +25 -x^2 -88 = 0
⇒3x^2 -20x -63 = 0
⇒3x^2 -27x+7x-63 =0
⇒3x(x-9) +7(x-9) = 0
⇒(3x+7)(x-9) =0
⇒x=9, x= -7/3 (as no. cant b -ve, so x=9)
Hence, smaller no = 9
& larger no = 2x-5 = 2*9-5 = 18-5 =13

Thanks
u'r welcm
2015-03-25T09:11:03+05:30

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Let the numbers be x (smaller) and y (larger).

According to the problem,

y² - x² = 88 ... (i)
y = 2x - 5 ... (ii)

Substituting the value of y from the equation (ii) in equation (i), we get,

(2x - 5)² - x² = 88
⇒ 4x² - 20x + 25 - x² - 88 = 0
⇒ 3x² - 20x - 63 = 0
⇒ 3x² - 27x + 7x - 63 = 0
⇒ 3x (x - 9) + 7 (x - 9) = 0
⇒ (3x + 7) (x - 9) = 0

∴ Either x = 9 or x = - 7/3
But x cannot be negative.
So, x = 9
And, y = 2x - 5 = 2 × 9 - 5 = 18 - 5 = 13