Question

If x is equals to 1 upon 2 minus root 3 find the value of x cube minus 2 x square - 7 x + 4

Answer 1

Answer:

Your required answer is 52

Step-by-step explanation:

x = 2 + √3  

1/x = 1/(2 + √3)  

= (2 -√3)/(2 +√3)(2 -√3)  

= (2 -√3)/(2² -√3²)  

= (2 - √3)

hence, x + 1/x = (2+√3)+(2-√3) = 4  

x³ + 1/x³ = (x + 1/x)³ -3(x + 1/x)  

= (4)³ - 3(4)  

= 64 -12  

= 52

Answer 2

QUESTION :-

If x = 1/2 - √3, find the value of x³ - 2 x 2 - 7x + 5

SOLUTION :-

x = 1/2-√3

Multiply the numerator and denominator by the conjugate of the denominator

x = 1/2-√3 x 2+√3/2+√3 = 2+√3/4-3 = 2+√3

⇒ x² = ( 2 + 3² ) = 4 + 4 √3 + 3 = 7 + 4 √3

Now consider the given expression

x³ - 2x² - 7x + 5

= x³ - 7x - 2x² + 5

= x ( x² - 7 )n- 2x² + 5

= ( 2 + √3 ) ( 7 + 4√3 - 7 ) - 2 ( 7 + 4√3 ) + 5

= ( 2 + √3 ) ( 4√3 ) - 14 - 8√3 + 5

= 8√3 + 12 - 14 - 8√3 + 5

= 3

QUESTION :-

If x = 1/2 - √3 , find the value of x³ - 2 x 2 - 7x + 4

SOLUTION :-

x = 2 + √3  

1/x = 1/(2 + √3)  

= (2 -√3)/(2 +√3)(2 -√3)  

= (2 -√3)/(2² -√3²)  

= (2 - √3)

hence, x + 1/x = (2+√3)+(2-√3) = 4  

x³ + 1/x³ = (x + 1/x)³ -3(x + 1/x)  

= (4)³ - 3(4)  

= 64 -12  

= 52

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