# sqrt(2x+9)-sqrt(x-4)=3 i am unable to solve dis icse math question could anyone help me put plz!?

• sqrt(2x+9)-sqrt(x-4)=3 i am unable to solve dis icse math question could anyone help me put plz!?

Answer #1 | 10/02 2014 09:58
x=8, x=20 see step by step solution: http://symbolab.com/solver/equation-calculator/Sqrt(2x%2B9)-sqrt(x-4)%3D3 hope this helps
Answer #2 | 10/02 2014 09:29
√(2x+9) - √(x-4) = 3 [ √(2x+9) - √(x-4) ]^2 = 3^2 . . . . . . . square each side (2x+9) - 2√(2x+9)√(x-4) + (x-4) = 9 3x + 5 - 2√(2x+9)√(x-4) = 9 . . . . . .- 2√(2x+9)√(x-4) = 4 - 3x . . . . get √ alone on one side . . . . . . .2√(2x+9)√(x-4) = 3x - 4 [2√(2x+9)√(x-4)]^2 = [3x - 4]^2 . . . . . . . square each side . . . . . 4(2x+9)(x-4) = 9x^2 - 24x + 16 . . . 8x^2 + 4x - 144 = 9x^2 - 24x + 16 . . . subtract right side from left . . . -x^2 + 28x - 160 = 0 x = [ -b +/- √(b^2 - 4ac) ] / 2a . = [ -28 +/- √(28^2 - 4*-1*-160) ] / -2 . = [ -28 +/- √144 ] / -2 . = [ -28 +/- 12 ] / -2 . = 20 and 8
Answer #3 | 10/02 2014 20:07
Sqrt (2x + 9) - sqrt (x - 4) = 3 Sqrt (2x + 9) = sqrt (x - 4) + 3 Squaring both sides, 2x + 9 = (x - 4) + 9 + 6 sqrt (x - 4) 6 sqrt (x - 4) = x + 4 Squaring both sides again, 36(x - 4) = x^2 + 8x + 16 x^2 - 28x + 160 = 0 (x - 20)(x - 8) = 0 Solutions: x = 8 x - 20
Answer #4 | 10/02 2014 22:54
(2x+9)^1/2 -( x- 4)^1/2 = 3 squaring on both sides 2x+9 - 2 [(2x+9)(x-4)}^1/2 + x- 4 =9 or3x - 4 = 2{2x^2+ x- 36}^1/2 again squaring on both sides 9x^2 - 24x + 16 = 8x^2+4x -144 or x^2 - 28x + 160 =0 or x^2 - 20x - 8x + 160 =0 or x( x - 20) - 8 ( x- 20)=0 or ( x- 20 ) ( x- 8) =0 so x= 8 & 20 ANSWER
Answer #5 | 11/02 2014 05:41
√(2x + 9) - √(x - 4) = 3 => √(2x + 9) = 3 + √(x - 4) Squaring both sides we have : 2x + 9 = 9 + (x - 4) + 2*3√(x - 4) => 2x - (x - 4) = 6√(x - 4) => x + 4 = 6√(x - 4) Again, squaring both sides, we get x² + 8x + 16 = 36(x - 4) => x² + 8x + 16 = 36x - 144 => x² - 28x + 160 = 0 => x² - 20x - 8x + 160 = 0 => x(x - 20) - 8(x - 20) = 0 => (x - 20)(x - 8) = 0 => (i) x - 20 = 0 , or (ii) x - 8 = 0 => (i) x = 20, or (ii) x = 8