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प्रश्न
If x = `(4 - sqrt(15))`, find the values of
`x^3 + (1)/x^3`
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उत्तर
`x^3 + (1)/x^3`
`(x^3 + (1)/x^3) = (x + (1)/x)^3 -3(x + (1)/x)` -----(1)
we will first find the value of `x + (1)/x`
`x + (1)/x = (4 - sqrt(15)) + (1)/((4 - sqrt(15))`
= `((4 - sqrt(15))^2 + 1)/((4 - sqrt(15))`
= `(16 + 15 - 8sqrt(15) + 1)/((4 - sqrt(15))`
= `(8(4 - sqrt(15)))/((4 - sqrt(15))`
= 8
substituting the valuesin (1)
`(x^3 + (1)/x^3) = (x + (1)/x)^3 -3(x + (1)/x)`
= 83 - 24
= 488
`(x^3 + (1)/x^3)` = 488
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संबंधित प्रश्न
Rationalize the denominator.
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`(5 + sqrt(6))/(5 - sqrt(6)`
Simplify the following
`(sqrt(5) - 2)/(sqrt(5) + 2) - (sqrt(5) + 2)/(sqrt(5) - 2)`
In the following, find the values of a and b:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = "a" + "b"sqrt(3)`
In the following, find the values of a and b:
`(sqrt(11) - sqrt(7))/(sqrt(11) + sqrt(7)) = "a" - "b"sqrt(77)`
In the following, find the value of a and b:
`(sqrt(3) - 1)/(sqrt(3) + 1) + (sqrt(3) + 1)/(sqrt(3) - 1) = "a" + "b"sqrt(3)`
Simplify:
`(sqrt(x^2 + y^2) - y)/(x - sqrt(x^2 - y^2)) ÷ (sqrt(x^2 - y^2) + x)/(sqrt(x^2 + y^2) + y)`
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
Show that: `x^3 + 1/x^3 = 52`, if x = 2 + `sqrt3`
