A Quadratic Equation Question with no Solutions

Topic : Solve for x

Question : √ (x-8) +√ x = 2

Answer :
Sometimes we get problems of the following type. After doing the problem You find that your solution does not match the condition.
√ (x-8) +√x= 2
√ (x-8) = 2- √x
Squaring
x-8= 4 – 4√x +x
-12= -4√x
√x=3
(√x)²=(3)²
x = 9
Since we find that this does not lead to negative numbers within Square root we are surprised when we find it does not match the problem condition
√1 + √9 = 4 not equal to 2
Confidently we must be able to assert that there is no solution.

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