If x -4-15- Find the value of x 2-1- x 2A- 58B- 60C- 62D- 32

The correct option is C 62(x^2+1/x^2) = (x + 1/x )^2 2 = (4+ √(15)+ 1/4+ √(15) )^2 2 = ((4+ √(15))+ (4 √(15))/(4+√(15)) × (4 √(15)) )^2 2 = (4+ √(15)+4 √(1 ...

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Byju's Answer

Standard XII

Physics

Definite Integrals

If x =4+√15, ...

Question

If $x = 4 + \sqrt{15}, Find the value of (x^{2} + \frac{1}{x^{2}})$

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Solution

The correct option is C 62
$(x^{2} + \frac{1}{x^{2}}) = {(x + \frac{1}{x})}^{2} - 2 = {(4 + \sqrt{15} + \frac{1}{4 + \sqrt{15}})}^{2} - 2 = {((4 + \sqrt{15}) + \frac{(4 - \sqrt{15})}{(4 + \sqrt{15}) \times (4 - \sqrt{15})})}^{2} - 2 = (4 + \sqrt{15} + 4 - \sqrt{15})^{2} - 2 = 8^{2} - 2 = 62$

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If x=4+√15,Find the value of (x2+1x2)

The correct option is C 62(x2+1x2)=(x+1x)2−2=(4+√15+14+√15)2−2=((4+√15)+(4−√15)(4+√15)×(4−√15))2−2=(4+√15+4−√15)2−2=82−2=62

If $x = 4 + \sqrt{15}, Find the value of (x^{2} + \frac{1}{x^{2}})$

The correct option is C 62
$(x^{2} + \frac{1}{x^{2}}) = {(x + \frac{1}{x})}^{2} - 2 = {(4 + \sqrt{15} + \frac{1}{4 + \sqrt{15}})}^{2} - 2 = {((4 + \sqrt{15}) + \frac{(4 - \sqrt{15})}{(4 + \sqrt{15}) \times (4 - \sqrt{15})})}^{2} - 2 = (4 + \sqrt{15} + 4 - \sqrt{15})^{2} - 2 = 8^{2} - 2 = 62$