2007-02-22 17:18:58 · 7 answers · asked by lirael1019 1 in Science & Mathematics ➔ Mathematics
Move sqrt(x-3) to the right
sqrt(x+3) = 3 - sqrt(x-3)
Square both sides of the equation
x+3 = 9 - 6sqrt(x-3) + (x-3) (Used the foil on the right)
Simplify; subtract 9
x-6 = -6sqrt(x-3) + (x-3)
subtract x and add 3
-3 = -6sqrt(x-3)
divide by -6
1/2 = sqrt(x-3)
square both sides again
1/4 = x-3
add 3
x = 13/4 or 4 and 1/3
2007-02-22 17:31:25 · answer #1 · answered by lizzie 3 · 2⤊ 0⤋
So, ?(x + 3) +?x = 3 there's a lot of distinctive the form you're able to try this. permit's look at one: approach ONE: sq. the two sides, so [?(x + 3) +?x]² = 3² (x + 3) + 2?(x + 3)?x + x = 9 x + 3 + 2?(x + 3)?x + x = 9 2x + 3 + 2?(x + 3)?x = 9 2x + 2?(x + 3)?x = 6 2[x + ?(x + 3)?x] = 6 x + ?(x + 3)?x = 3 ?(x + 3)?x = 3 – x combine sq. roots; ?a?b = ?(ab), so ?(x + 3)?x = 3 – x ?(x(x + 3)) = 3 – x ?(x² + 3x) = 3 – x Now, sq. the two sides back, so [?(x² + 3x)]² = (3 – x)² x² + 3x = 9 – 6x + x² 3x = 9 – 6x 9x = 9 x = one million examine recommendations so, For x = one million, ?(one million + 3) +?one million = 3 ?(4) + one million = 3 2 + one million = 3 3 = 3 the respond is x = one million. In precis, you should sq. the two sides two times. approach 2: ?(x + 3) + ?x = 3 Subtract ?x from the two sides, so ?(x + 3) = 3 – ?x Squaring the two sides, [?(x + 3)]² = [3 – ?x]² x + 3 = 9 – 6?x + x 3 = 9 – 6?x -6 = -6?x one million = ?x Squaring, the two sides, one million² = [?x]² x = one million So, the respond is x = one million wish that helps.
2016-12-18 09:06:14 · answer #2 · answered by roedel 3 · 0⤊ 0⤋
just an addition to lizzie's answer,
there should be 2 answers; but one of them may be disqualified because it involves imaginary numbers
sqrt (x+3) + sqrt (x-3) = 3
square both sides
x+3 + 2(sqrt (x+3)(x-3)) + x-3 = 9
2x + 2 sqrt (x^2 - 9) = 9
9-2x = 2 * sqrt (x^2 - 9)
9/2 - x = sqrt (x^2 -9)
x^2 -9 = x^2 - 9x + 81/4
9x = 9 + 81/4
x = 1+ 9/4 = 13/4
only 1 root because x^2 was canceled out.
2007-02-22 17:40:42 · answer #3 · answered by martianunlimited 2 · 0⤊ 0⤋
x = 13/4
2007-02-22 17:34:00 · answer #4 · answered by a_liberal_economist 3 · 0⤊ 0⤋
(√x + 3) + (√x - 3) = 3
2√x = 3
√x = 3/2
x = 9/4
2007-02-22 20:12:44 · answer #5 · answered by Como 7 · 0⤊ 0⤋
add and get 2 sqrt(x) = 3
or sqrt x = 3/2
so x = 9/4
2007-02-22 17:21:31 · answer #6 · answered by Mein Hoon Na 7 · 0⤊ 2⤋
√x+3+√x-3=3 combine like terms
2√x=3 square both sides
4x=9 divide both sides by 4
x=9/4=2.25
2007-02-22 17:28:15 · answer #7 · answered by yupchagee 7 · 0⤊ 2⤋