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प्रश्न
If x = `(7 + 4sqrt(3))`, find the value 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 out `x + (1)/x`
`x + (1)/x = (7 + 4sqrt(3)) + (1)/((7 + 4sqrt(3))`
= `((7 + 4sqrt(3))^2 + 1)/((7 + 4sqrt(3))`
= `(49 + 48 + 56sqrt(3) + 1)/((7 + 4sqrt(3))`
= `(98 + 56sqrt(3))/((7 + 4sqrt(3))`
= `(14(7 + 4sqrt(3)))/((7 + 4sqrt(3))`
= 14
Substituting in (1)
`(x^3 + (1)/x^3) = (x + (1)/x)^3 - 3(x + (1)/x)`
= (14)3 – 3 × 14
= 2744 – 42
= 2702
∴ `(x^3 + (1)/x^3) = 2702`
संबंधित प्रश्न
Rationalize the denominator.
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Simplify by rationalising the denominator in the following.
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Simplify by rationalising the denominator in the following.
`(3 - sqrt(3))/(2 + sqrt(2)`
In the following, find the values of a and b.
`(sqrt(3) - 1)/(sqrt(3) + 1) = "a" + "b"sqrt(3)`
In the following, find the values of a and b:
`(sqrt(3) - 2)/(sqrt(3) + 2) = "a"sqrt(3) + "b"`
If x = `(4 - sqrt(15))`, find the values of
`x + (1)/x`
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
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Draw a line segment of length `sqrt8` cm.
