If `sqrt (x+3) + sqrt (x-2) = 5` , then the value of x is ____ ?
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`sqrt(x+3) + sqrt(x-2) = 5`
To remove the radicals, perform the opposite operation of square root. So, take the square of both sides.
`(sqrt(x+3) + sqrt(x-2))^2 = 5^2`
`x+3 + 2sqrt(x+3)*sqrt(x-2) + x-2=25`
Then, isolate the radical term.
Take the square of both sides again to eliminate the radicals.
Note that the terms `4x^2` appears on both sides of the equation. So if we move the `4x^2` from the right to left, the resulting expression is:
Then, bring together the terms with x on one side of the equation. Also, bring together the terms without x on the opposite side of the equation.
Then, isolate x.
Hence, the value of x is 6.
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