Can someone helpe me solve this equation . Help me break it down please..becuase i have tried to do it mnay times but have fallen short...
[SQRT(x + 3)] - [SQRT(x - 2)] =1
[SQRT(x + 3)] =1 + [SQRT(x - 2)]
I think. then you gotta do the rest.
√(x+3) = 1 + √(x-2)
now square both sides
x+3 = 1 + 2√x-2) + x-2
2√x-2) = 4
√(x-2) = 2
square again
x-2 = 4
x = 6
check:
LS = √9 - √4
= 3-2 = 1 = RS
so x = 6
Sure, I can help you break down and solve this equation step by step.
The given equation is:
√(x + 3) - √(x - 2) = 1
To solve this equation, you need to isolate the variable, x. Let's start by getting rid of the square roots.
1. Firstly, let's move the term √(x - 2) to the other side of the equation:
√(x + 3) = √(x - 2) + 1
2. Next, square both sides of the equation to eliminate the square roots:
(√(x + 3))^2 = (√(x - 2) + 1)^2
Squaring both sides will give us:
x + 3 = (x - 2) + 2√(x - 2) + 1
3. Simplify the equation:
x + 3 = x - 2 + 2√(x - 2) + 1
Combine like terms and isolate the radical term:
x - x + 3 + 2 - 1 = 2√(x - 2)
4. Simplify further:
4 = 2√(x - 2)
5. Divide both sides by 2 to solve for the radical term:
2 = √(x - 2)
6. Now, square both sides to eliminate the square root:
(√2)^2 = (√(x - 2))^2
2 = x - 2
7. Move the constant term to the other side of the equation:
2 + 2 = x
8. Finally, simplify to get the solution:
x = 4
Therefore, the solution to the equation is x = 4.
Remember to always double-check your solution by substituting it back into the original equation to make sure it satisfies the equation.
Let me know if you need any further assistance!