Is this right...
Square root X+6 - Square root X =Square root 2.
I did X+6 = (Square root 2+Square root X )(Square root 2+Square root X ).
Then I did X+4=2 Square root 2+X. THEN i GOT 2. IS THAT RIGHT??
no, if you try x=2 in your starting equation it will not work.
X+6 = (Square root 2+Square root X )(Square root 2+Square root X ) was right
x+6 = 2 + 4√x + x
4 = 4√x
1 = √x
x = 1
try it in the original question
√8 - √2
= 2√2 - √2
= √2
= right side
thanks reiny, you are very smart!
Let's break down your solution and determine if it is correct.
Step 1: You started by square rooting both sides of the equation:
√(X+6) - √X = √2
This is the correct step.
Step 2: You squared both sides of the equation:
(X+6) = (√2 + √X) (√2 + √X)
This is also correct. Squaring both sides allows you to eliminate the square roots.
Step 3: You simplified the right side of the equation:
(X+6) = (2 + 2√2√X + X)
This is correct. When multiplying two square root terms (√2 and √X), you multiply the coefficients (2 and X) and the square roots (√2 and √X), resulting in 2√2√X.
Step 4: You simplified the equation further:
X+6 = 2 + 2√2√X + X
Here, you correctly combined like terms on both sides of the equation.
Step 5: You subtracted X from both sides of the equation:
6 = 2 + 2√2√X
This step is correct.
However, when you said you got 2, it seems you may have made an error in your calculations. Let's continue to solve the equation:
Step 6: You subtracted 2 from both sides of the equation:
6 - 2 = 2√2√X
This simplifies to: 4 = 2√2√X
Step 7: You divided both sides of the equation by 2:
4/2 = √2√X
This simplifies to: 2 = √2√X
Step 8: You squared both sides of the equation again to eliminate the square root:
(2)^2 = (√2√X)^2
This simplifies to: 4 = 2√X
Step 9: You divided both sides of the equation by 2:
4/2 = √X
This simplifies to: 2 = √X
Step 10: You squared both sides of the equation once more:
(2)^2 = (√X)^2
This simplifies to: 4 = X
So the final solution is X = 4. Therefore, your initial answer of X = 2 was incorrect. The correct solution is X = 4.