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: ]

youll have to do them both.x=2y-5x=2(9)-5x=18-5x=13 when y=9x=2y-5x=2(-7/3)-5x=(-14/3)-5x=(-14/3)-(15/3)x=-29/3 when y=-7/3-x^2 - y^2 = 88x = 2y-5---Place 2y-5 in for x---(2y-5)^2-y^2=88(2y-5)(2y-5) - y^2=884y^2-20y+25-y^2=883y^2-20y+25=88Make equation equal to 0:3y^2-20y-63=0(3y-7)(y-9) -----> Check your work by multiplying to see if you get the original equation: (3y-7)(y-9) = 3y^2-20y-63 -- Its the same thing as the original therefore it is correctNow using the zero product property, one of the two members of the equation MUST be equal to zero. So we set each one equal to 0:3y-7=0 3y=7y=3/7y-9=0y=9then plugging these back in for x, we get:x=2(7/3)-5x=14/3-15/3x=-1/3x=2(9)-5x=18-5x=13The solution is: 9,13or-1/3,......

numbers .

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Let x = one number
Let y = the other number

Given: x^2-y^2=88 and x=2y-5
Find: x and y

x^2-y^2=88
(2y-5)^2-y^2=88
(2y-5)(2y-5)-y^2=88
4y^2-10y-10y+25-y^2=88
3y^2-20y+25=88
3y^2-20y+25-88=0
3y^2-20y-63=0
(3y+7)(y-9)=0
3y+7=0 or y-9=0
3y=0-7 or y=0+9
3y=-7 or y=9
y=-7/3 or y=9

Plug in the value of y into either of the two equations you started with. Since you have two possible values of y, you'll have to do them both.

x=2y-5
x=2(9)-5
x=18-5
x=13 when y=9

x=2y-5
x=2(-7/3)-5
x=(-14/3)-5
x=(-14/3)-(15/3)
x=-29/3 when y=-7/3

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

---Place 2y-5 in for x---
(2y-5)^2-y^2=88

(2y-5)(2y-5) - y^2=88

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

3y^2-20y+25=88

Make equation equal to 0:

3y^2-20y-63=0

(3y-7)(y-9) -----> Check your work by multiplying to see if you get the original equation:
(3y-7)(y-9) = 3y^2-20y-63 -- Its the same thing as the original therefore it is correct

Now using the zero product property, one of the two members of the equation MUST be equal to zero. So we set each one equal to 0:

3y-7=0
3y=7
y=3/7

y-9=0
y=9

then plugging these back in for x, we get:
x=2(7/3)-5
x=14/3-15/3
x=-1/3

x=2(9)-5
x=18-5
x=13

The solution is: 9,13 or -1/3, 7/3

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LET THE SMALLER NUMBER BE X

LARGER NUMBER = 2X -5

( 2X-5)^2 - X^2 = 88

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

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

ANSWER NUMBERS ARE 9 AND 13
CHECK
13^2 - 9^2 = 88

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let two numbers are x & y & let x > y
so x^2 - y^2 = 88------------------(I)
and x + 5 = 2y-------------------(II)

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