2007-10-03 16:39:17 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
There can't be any solutions for this (I assume we're dealing in real numbers here).
The easiest way to see why is to note that √(x+7) and √(x+2) are both more then √x, so the LHS is more than 2√x, but the RHS is less than √(x-1) and hence less than √x.
2007-10-03 16:44:31 · answer #1 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
sqrt(x+7) + sqrt(x+2) = sqrt(x-1) - sqrt(x-2)
square both sides...
x + 7 + sqrt(x+7)sqrt(x+2) + x + 2 = x - 1 - sqrt(x-1)sqrt(x-2) + x - 2
combining like terms,
12 + sqrt(x+7)sqrt(x+2) = - sqrt(x-1)sqrt(x-2)
squaring both sides again...
144 + 12sqrt(x+7)sqrt(x+2) + (x+7)(x+2) = (x-1)(x-2)
144 + 12sqrt(x+7)sqrt(x+2) + x^2 + 9x + 14 = x^2 - 3x + 2
again, combining like terms...
12sqrt(x+7)sqrt(x+2) = -12x - 156
dividing both sides by 12,
sqrt(x+7)sqrt(x+2) = -x - 13
squaring both sides finally (to eliminate the radical sign),
(x+7)(x+2) = x^2 + 26x + 169
x^2 + 9x + 14 = x^2 + 26x + 169
-17x = 155
x = -155/17
2007-10-03 23:52:58 · answer #2 · answered by tootoot 3 · 0⤊ 0⤋
I started by squaring both sides then adding common term, divideed by 2, sqaured both sides again, added common terms, divided by 2, squared again, combined common terms, divided by -36 and got x=2. Checked answer and it was false, so did a graph of the 2 sides of equation and decided there was no solution. if you need to see the work, i cansend it to you. don't know if this is right though.
2007-10-04 00:15:14 · answer #3 · answered by mdgtres_2000 1 · 0⤊ 0⤋
sqrt(x+7) +sqrt(x+2) = sqrt(x+7+x+2)=sqrt(2x+9)
sqrt(x-1)-sqrt(x-2)=sqrt(x-1-x+2)=sqrt(1)=sqrt
sqrt(2x+9)=sqrt...divide by sqrt
2x+9=1
x=-4
2007-10-03 23:55:01 · answer #4 · answered by gameplayer 2 · 0⤊ 1⤋