I need help solving this equation.
[SQRT(x + 3)] - [SQRT(x - 2)] =1
I know I am supposed to square each side however my teacher tells me I ahve to foil the lefthand side of the equation. Cna someone please help me with this.
Thank you.
well, if you square both sides
you get (FOIL)
x+3-2sqrt(x-2)sqrt(x+3) + x-2=1
2x+2- 2sqrt( x^2+x-6)=1
or 2x+2-2=2sqrt(x^2+x-6)
square both sides
4x^2=4(x^2+x-6)
x=6
Thank you.
Would I do the same thing with this equation?
[SQRT(x + 7)] - 2[SQRT(x)] =-2
Beacause I see what you have showed me BUt i am stll a little bit confused. Please if you have the time help me. Thank you.
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To solve the equation [SQRT(x + 3)] - [SQRT(x - 2)] = 1, you are correct that squaring both sides of the equation is one way to proceed. However, instead of using FOIL (First, Outer, Inner, Last) to multiply the terms involving square roots, we can simplify the equation by isolating one square root term on one side. Here's the step-by-step solution:
1. Start with the original equation: [SQRT(x + 3)] - [SQRT(x - 2)] = 1.
2. Move the second square root term to the right-hand side of the equation:
[SQRT(x + 3)] = [SQRT(x - 2)] + 1.
3. Square both sides of the equation to eliminate the square roots:
[SQRT(x + 3)]^2 = ([SQRT(x - 2)] + 1)^2.
4. Simplify the left-hand side:
(x + 3) = ([SQRT(x - 2)] + 1)^2.
5. Expand the right-hand side of the equation using the property (a + b)^2 = a^2 + 2ab + b^2:
(x + 3) = [SQRT(x - 2)]^2 + 2([SQRT(x - 2)])(1) + 1^2.
6. Simplify the right-hand side:
(x + 3) = (x - 2) + 2[SQRT(x - 2)] + 1.
7. Combine like terms and simplify:
x + 3 = x - 2 + 2[SQRT(x - 2)] + 1.
8. Cancel out the x terms on both sides of the equation:
3 = -2 + 2[SQRT(x - 2)] + 1.
9. Combine like terms:
3 = -1 + 2[SQRT(x - 2)].
10. Move the constant term to the other side:
2[SQRT(x - 2)] = 3 + 1.
11. Simplify:
2[SQRT(x - 2)] = 4.
12. Divide by 2:
[SQRT(x - 2)] = 2.
13. Square both sides once more to eliminate the square root:
([SQRT(x - 2)])^2 = 2^2.
14. Simplify:
x - 2 = 4.
15. Solve for x:
x = 4 + 2.
16. Final solution:
x = 6.
So the solution to the equation [SQRT(x + 3)] - [SQRT(x - 2)] = 1 is x = 6.