square root of 2+(square root of 1+k)equals the square root of 5. Solve for k
I read that as
√2 + √(1+k) = √5
√1+k = √5 - √2
square both sides
1+k = 5 - 2√10 + 2
k = 6 - 2√10 or appr -0.325
please help me compare fraction
sure
To solve for k in the equation √2 + √(1 + k) = √5, follow these steps:
Step 1: Start by isolating √(1 + k) on one side of the equation.
Subtract √2 from both sides:
√(1 + k) = √5 - √2
Step 2: Square both sides of the equation to eliminate the square root on the left side.
(√(1 + k))^2 = (√5 - √2)^2
1 + k = 5 - 2√5√2 + 2
Step 3: Simplify the terms within the parentheses on the right side.
1 + k = 7 - 2√10
Step 4: Move the constant term to the right side by subtracting 1 from both sides.
k = 7 - 2√10 - 1
Step 5: Combine like terms on the right side to simplify the equation.
k = 6 - 2√10
Thus, the solution for k is k = 6 - 2√10.