Question 1209931: Find x, giving your answer in the form a + square root(b)
2 = x(squareroot(7)-3)
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's solve for x:
2 = x(√7 - 3)
To isolate x, we need to divide both sides by (√7 - 3):
x = 2 / (√7 - 3)
Now, we need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of (√7 - 3), which is (√7 + 3):
x = 2(√7 + 3) / [(√7 - 3)(√7 + 3)]
Now, let's simplify the denominator:
(√7 - 3)(√7 + 3) = (√7)² - (3)² = 7 - 9 = -2
Now, substitute this back into the expression for x:
x = 2(√7 + 3) / (-2)
Divide both the numerator and the denominator by 2:
x = (√7 + 3) / (-1)
x = -√7 - 3
Rearrange to the desired form a + √b:
x = -3 - √7
Therefore, x = -3 - √7.
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