Solve for x square root of x+4+ square root of x-1=5

Problem

√(,x+4)+√(,x−1)=5

Solution

1. Isolate one of the radical terms by subtracting √(,x−1) from both sides of the equation.

√(,x+4)=5−√(,x−1)

2. Square both sides of the equation to eliminate the radical on the left side.

(√(,x+4))2=(5−√(,x−1))2

3. Expand the right side using the identity (a−b)2=a2−2*a*b+b2

x+4=25−10√(,x−1)+(x−1)

4. Simplify the equation by combining like terms and isolating the remaining radical term.

x+4=x+24−10√(,x−1)

4=24−10√(,x−1)

−20=−10√(,x−1)

5. Divide both sides by −10 to further isolate the radical.

2=√(,x−1)

6. Square both sides again to solve for x

2=(√(,x−1))2

4=x−1

7. Solve for x by adding 1 to both sides.

x=5

8. Check the solution by substituting x=5 back into the original equation.

√(,5+4)+√(,5−1)=√(,9)+√(,4)

3+2=5

Final Answer

√(,x+4)+√(,x−1)=5⇒x=5

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