# (x-5)(x-6)=25/576 solve for x

2
by danerstiker47

2014-10-03T19:09:16+05:30
(x-5)(x-6) = 25/567
⇒  x²-6x-5x+30 = 5/24
x²-10x+25-(x-5) = 5/24
⇒  (x-5)²-(x-5)-(5/24)² = 0
⇒   y²-y-(5/24)² = 0
⇒   y²-25y/24+y/24-5²/24² = 0
⇒      y(y-25/24) 1/24(y-25/24) = 0
⇒      (y-25/24)(y+1/24) = 0
⇒     y-25/24 = 0 ,   then  y = 25/24
therefore,    x-5 = 25/24 ,⇒  x = 25/24+5 = 145/24
And  y+1/24 = 0,   then y = -1/24
therefore,   x-5 = -1/24 ,  ⇒   x = 5-1/24 = 119/24
the values of x are 145/24 and 119/24
try to put your answers in the equations. It won't satisfy the equation.
ok i try
oh yes i mis calculated
thank you
2014-10-03T19:42:59+05:30

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Take (x-6) = t
then (x-5) = (t+1)

(x-5)+(x-6) = 25/576
⇒(t+1)t = 25/576

⇒t² + t -  = 0

t =  and

or t =  and

But t = (x-6)
case: 1
t = 1/24
⇒x-6 = 1/24
⇒x = 6 + 1/24
⇒x = (144+1)/24
x = 145/24
case: 2
t = -25/24
⇒x-6 = -25/24
⇒x = 6 -25/24
⇒x = (144-25)/24
x = 119/24

ITOO DID IN THE SAME WAY