sqrt(x+7)=x+1
2007-02-22 00:46:04 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
sqrt(x+7)=(x+1)
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x+7=(x+1)^2
x+7=x^2+2x+1
0=x^2+2x-x+1-7
X^2+x-6=0
solve x by factoring
X^2+x-6=0
(x+3)(x-2)=0
x1=-3
x2=2
2007-02-22 00:57:48 · answer #1 · answered by jAmPr0tzz 2 · 0⤊ 0⤋
First of all since sqrt is done of x+7 ....
Therefore x+7 >=0.........(1)
sqraing both sides now.....
X+7= X^2+2 * X + 1.....
X^2 + X - 6 = 0......(2) solve with b= -1, a= 1, c= -6
we have x= ( -1 + sqrt( 1+24) ) / ( -2) and ( -1 - sqrt(1+24) )/( -2)
this gives 2 values for X as -3 and 2 and both satisfies (1).
2007-02-22 08:58:10 · answer #2 · answered by the_gr8_1 3 · 0⤊ 0⤋
Squaring both sides will give:
x+7 = (x+1)(x+1)
x+7 = x^2 + 2x +1
0 = x^2 +x -6
and voila-a nice quadratic equation.
Solve by using formula or factorising to (x-2)(x+3) = 0 giving x = 2 or -3
Technically speaking sqrt will only give positive root, so x=2 is the only correct answer
Hope this helps!
2007-02-22 08:53:53 · answer #3 · answered by mustafa 2 · 0⤊ 0⤋
x = 2
2007-02-22 08:49:25 · answer #4 · answered by tony1athome 5 · 0⤊ 2⤋
Square both sides: -
x + 7 = (x + 1)²
x + 7 = x² + 2x + 1
x² + x - 6 = 0
(x + 3).(x - 2) = 0
x = - 3, x = 2
2007-02-22 08:52:01 · answer #5 · answered by Como 7 · 1⤊ 0⤋
put at power 2
x+7 = (x+1)^2 = x^2+2x+1
x^2+x -6 =0 roots -1 +/- (1+24)^0.5/2 -3 and 2
it works
2007-02-22 08:52:17 · answer #6 · answered by maussy 7 · 0⤊ 0⤋