Difference of sq of two numbers is 88 . if the larger no. is 5 less than twice the smaller no. , find the two

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Difference of sq of two numbers is 88 . if the larger no. is 5 less than twice the smaller no. , find the two

[From: ] [author: ] [Date: 11-10-09] [Hit: ]

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so from (I) & (II) (2y - 5)^2 - y^2 = 88
4y^2 - 20 y + 25 - y^2 = 88
or 3y^2 - 20 y - 63 = 0
3y^2 - 27 y + 7y - 63 =0
3y ( y - 9 ) + 7 ( y- 9) = 0
so y = 9 [ & y = -7/3 discarded]
so x = 13
so two numbers are ------- 13 & 9 ans,
proof---------- (169 - 81 = 88 ]

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let the smaller number be x
then larger number=[2x- 5]
now,

[2x--5]^2-x^2= 88

4x^2--20x +25 --x^2=88

3x^2 -- 20x +25-88=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

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x^2 - y^2 = 88
x = 2y - 5

(2y - 5)^2 -y^2 = 88
4y^2 + 25 - y^2 = 88
3y^2 = 63
y^2 = 21
y = 4.58
x = 4.16

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