Solve for x square root of x^2+8-3=0

Problem

√(,x2+8)−3=0

Solution

1. Isolate the radical term by adding 3 to both sides of the equation.

√(,x2+8)=3

2. Square both sides of the equation to eliminate the square root.

(√(,x2+8))2=3

x2+8=9

3. Isolate the x2 term by subtracting 8 from both sides.

x2=1

4. Solve for x by taking the square root of both sides, remembering to include both the positive and negative roots.

x=±√(,1)

x=1,x=−1

5. Verify the solutions by substituting them back into the original equation. For x=1 √(,1+8)−3=√(,9)−3=0 For x=−1 √(,(−1)2+8)−3=√(,9)−3=0 Both are valid.

Final Answer

√(,x2+8)−3=0⇒x=±1

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