Final answer:
To solve the equation √x+9=6-√√x-2, we can square both sides and simplify the equation to find the value of x.
Step-by-step explanation:
In this question, we are given the equation √x+9=6-√√x-2. To solve this equation, we can start by squaring both sides. Squaring the left side of the equation, we get (√x+9)^2=x+9. On the right side, we need to apply the distributive property to the negative sign and square root: (6-√√x-2)^2=(6-(√x-2))^2=(6-(√x-2))(6-(√x-2))=36-12(√x-2)+(√x-2)^2=36-12(√x-2)+(x-2).
Therefore, we now have the equation x+9=36-12(√x-2)+(x-2). Simplifying this equation further, we combine like terms and isolate the radical term to one side: x+9=34+x-14-12(√x-2). We can now cancel out like terms on both sides of the equation: 9-34+14=-12(√x-2).
Simplifying further, we find that -11=-12(√x-2). Dividing both sides of the equation by -12, we get √x-2=-11/-12, which simplifies to √x-2=11/12. Squaring both sides again, we have x-2=(11/12)^2. Expanding the right side, we get x-2=121/144. Adding 2 to both sides, we find x=121/144+2.
Therefore, the solution to the equation √x+9=6-√√x-2 is x=121/144+2.
Learn more about Solving equations involving square roots