- #1
ryn droma
- 1
- 0
I don't understand why this is a no solution
original problem
√(x-5) - √(x-8) = 3
My solution attempt
add +√(x-8) to both sides:
√(x-5) - √(x-8) = 3
√(x-5) = 3 + √(x-8)
squaring both sides:
(√(x-5))^2 = (3 + √(x-8))^2
FOIL out the right side:
x - 5 = 3^2 + 2(3√(x-8)) + √(x-8)^2
simplify:
x - 5 = 9 + 6√(x-8) + x - 8
combine like terms:
x - 5 = x + 1 + 6√(x-8)
Subtract x and 1 from both sides:
x - 5 = x + 1 + 6√(x-8)
-6 = 6√(x-8)
divide both sides by 6:
-1 = √(x-8)
At this point, is it the -1 that means no solution?
I continued with squaring both sides again:
(-1)^2 = √(x-8)^2
1 = x - 8
+8
x = 9
original problem
√(x-5) - √(x-8) = 3
My solution attempt
add +√(x-8) to both sides:
√(x-5) - √(x-8) = 3
√(x-5) = 3 + √(x-8)
squaring both sides:
(√(x-5))^2 = (3 + √(x-8))^2
FOIL out the right side:
x - 5 = 3^2 + 2(3√(x-8)) + √(x-8)^2
simplify:
x - 5 = 9 + 6√(x-8) + x - 8
combine like terms:
x - 5 = x + 1 + 6√(x-8)
Subtract x and 1 from both sides:
x - 5 = x + 1 + 6√(x-8)
-6 = 6√(x-8)
divide both sides by 6:
-1 = √(x-8)
At this point, is it the -1 that means no solution?
I continued with squaring both sides again:
(-1)^2 = √(x-8)^2
1 = x - 8
+8
x = 9