Question

(x-2 root 6)(5root 3+5 root 2)/5root3-5root2) is 1. Find x​

Answer 1

Answer:

(x-2√6)(5√3+5√2)/(5√3-5√2) = 1

Step-by-step explanation:

(x-2√6)(5√3+5√2) = 1(5√3-5√2)

(x-2√6) = 5(√3-√2)/5(√3+√2)

rationalize

(x-2√6) = (√3)^2 + (√2)^2 - 2(√3)(√2)/(√3)^2 - (√2)^2

(x-2√6) = 3 + 2 - 2√6

x = 5 - 2√6 + 2√6

x = 5

The answer is x = 5

Answer 2

Answer:

5

Step-by-step explanation:

$\frac{(x - 2\sqrt{6} )(5\sqrt{3} + 5\sqrt{2} )}{5\sqrt{3} - 5\sqrt{2} }$  = 1

$(x-2\sqrt{6} )(5\sqrt{3} + 5\sqrt{2)} = (5\sqrt{3} - 5\sqrt{2)}$

$(x-2\sqrt{6} ) = \frac{(5\sqrt{3} - 5\sqrt{2)}}{(5\sqrt{3} + 5\sqrt{2)}}$

$(x-2\sqrt{6} ) = \frac{5(\sqrt{3} - \sqrt{2)}}{5(\sqrt{3} + \sqrt{2)}}$

We cancel the 5,

$(x-2\sqrt{6} ) = \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}$

Rationalizing the denominator, we get

$(x-2\sqrt{6} ) = \frac{(\sqrt{3} -\sqrt{2} )^{2}}{(\sqrt{3})^{2} - (\sqrt{2})^{2} }$

$(x-2\sqrt{6} ) = 3 + 2 -2\sqrt{6}$

$x = 3 + 2 -2\sqrt{6} +2\sqrt{6}$

$x= 5$