Question

if X equal to 2 + 3 root 2 then find the value of x + 14 upon x

Answer 1

x = 2 + 3√2

now

x + 14/x = 2+3√2 + 14/2+3√2

=> (2+3√2)² + 14 / 2+3√2

=> 4 + 9×2 + 2×2×3√2 +14 / 2+3√2

=> 4+18+12√2+14/2+3√2

=> 36+12√2/2+3√2

=> 12(3+√2)/√2(√2+3)

=> 12/√2

=> 6√2 ......Answer


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Hope it will help you ....✌✌

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Answer 2

Answer:

Required value of x is $6 \sqrt{2}$

Step-by-step explanation:

Given,$x = 2 + 3 \sqrt{2}$

Now we want to find value of $x + \frac{14}{x}$

So we are putting $x = 2 + 3 \sqrt{2}$in $x + \frac{14}{x}$

Now,$x + \frac{14}{x} = 2 + 3 \sqrt{2} + \frac{14}{2 + 3 \sqrt{2} }$

For removing irrational part from denominator,we are multiplying denominator and numerator by $2 - 3 \sqrt{2}$

So,$2 + 3 \sqrt{2} + \frac{14 \times (2 - 3 \sqrt{2} )}{(2 + 3 \sqrt{2})(2 - 3 \sqrt{2})}$

$2 + 3 \sqrt{2} + \frac{14 \times (2 - 3 \sqrt{2)} }{ {2}^{2} - {(3 \sqrt{2}) }^{2} }$

$= 2 + 3 \sqrt{2} + \frac{14(2 - 3 \sqrt{2})}{4 - 18}$

$= 2 + 3 \sqrt{2} - \frac{14(2 - 3 \sqrt{2})}{ - 14}$

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

$= 6 \sqrt{2}$