Question

If x= 7 - 4√3 then find the value of (a) (x+1/x) rais to 2 b) x rais 2+1/x rais to 2

Answer 1

The equation x = 7 - 4√3 is a radical expression, and the value of the radical expression is $(x + \frac 1x)^2 = 3650401 -2107560\sqrt 3$

How to solve the expressions?

The equation is given as:

x = 7 - 4√3

So, we have:

$(x + \frac 1x)^2 = (7 - 4\sqrt 3 + \frac{1}{7 - 4\sqrt 3})^2$

Take the LCM

$(x + \frac 1x)^2 = (\frac{49 -56\sqrt3 + 48}{7 - 4\sqrt 3})^2$

Evaluate the like terms

$(x + \frac 1x)^2 = (\frac{97 -56\sqrt3 }{7 - 4\sqrt 3})^2$

Rationalize

$(x + \frac 1x)^2 = (\frac{(97 -56\sqrt3)(7 - 4\sqrt 3) }{49 -48})^2$

Evaluate the difference

$(x + \frac 1x)^2 = ((97 -56\sqrt3)(7 - 4\sqrt 3))^2$

Expand

$(x + \frac 1x)^2 = (679 -388\sqrt 3 -392\sqrt 3 + 672)^2$

Evaluate the like terms

$(x + \frac 1x)^2 = (1351 -780\sqrt 3 )^2$

Expand

$(x + \frac 1x)^2 = 1825201 +1825200 -2107560\sqrt 3$

$(x + \frac 1x)^2 = 3650401 -2107560\sqrt 3$

Hence, the value of the radical expression is $(x + \frac 1x)^2 = 3650401 -2107560\sqrt 3$

Read more about radical expressions at:

brainly.com/question/8952483

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