how do you solve this:
√(x+6)-√(x-2) = 2
what is x?
show ur work
√(x+6)-√(x-2) = 2
what is x?
show ur work
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√(x+6)-√(x-2) = 2
√(x+6) = 2 + √(x-2) => square both sides, RS=> (a + b)^2 = a^2 + 2ab + b^2
x + 6 = 4 + x - 2 + 4√(x-2) => simplify
4√(x-2) = 4 => again square both sides
16x - 32 = 16
16x = 48
x = 3 => always check answers in the original equation:
√(3+6)-√(3-2) = 2
√(9)-√(1) = 2
3 - 1 = 2 => checks
x = 3 => Answer
√(x+6) = 2 + √(x-2) => square both sides, RS=> (a + b)^2 = a^2 + 2ab + b^2
x + 6 = 4 + x - 2 + 4√(x-2) => simplify
4√(x-2) = 4 => again square both sides
16x - 32 = 16
16x = 48
x = 3 => always check answers in the original equation:
√(3+6)-√(3-2) = 2
√(9)-√(1) = 2
3 - 1 = 2 => checks
x = 3 => Answer