Find the value of X if \(\frac{\sqrt{2}}{x+\sqrt{2}}=\fra...
Find the value of X if √2x+√2=1x−√2
3√2+4
3√2-4
3-2√2
4+2√2
Correct answer is A
Start your solution by cross-multiplying,
√2x+√2=1x−√2
[x - √2] √2 = x + √2
where √2×√2=2
x√2 - √2 * √2 = x + √2
then collect like terms
x√2 - x = √2 + 2
and factorize accordingly to get the unknown.
x(√2 - 1) = √2 + 2
x = √2+2√2−1
rationalize
x = √2+2√2−1 * √2+1√2+1
x = √4+√2+2√2+2√4+√2−√2−1
x = 2+3√2+22−1
x = 3√2+41
x = 3√2 + 4
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