50 POINTS!!!!!! PLS HELP ME ASAP
1 answer:
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The trick is to exploit the difference of squares formula,
Set a = √8 and b = √6, so that a + b is the expression in the denominator. Multiply by its conjugate a - b:
Whatever you do to the denominator, you have to do to the numerator too. So
Expand the numerator:
So we have
But √12 = √(3•4) = 2√3, so
Let us try and solve it analytically. We have that the side=x+3 together with the short side=s and the diagonal=x+4 satisfy the Pythagorean Theorem. Then we have that 
. This yields 
which yields s^2=2x+7, hence a) is the correct answer.
which yields s^2=2x+7, hence a) is the correct answer.