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प्रश्न
Expand.
`(x + 1/x)^3`
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उत्तर
Here, a = x, b = `1/x`
We know that,
(a + b)3 = a3 + 3a2b + 3ab2 + b3
∴ `(x + 1/x)^3 = x^3 + 3(x)^2(1/x) + 3(x)(1/x)^2 + (1/x)^3`
= `x^3 + 3x^2 xx 1/x + 3x xx 1/x^2 + 1/x^3`
= `x^3 + 3x + 3/x + 1/x^3`
∴ `(x + 1/x)^3 = x^3 + 3x + 3/x + 1/x^3`
संबंधित प्रश्न
Expand.
(k + 4)3
Find the cube of : `2a + 1/(2a)` ( a ≠ 0 )
If `a^2 + 1/a^2` = 18; a ≠ 0 find :
(i) `a - 1/a`
(ii) `a^3 - 1/a^3`
If a + 2b = 5; then show that : a3 + 8b3 + 30ab = 125.
Two positive numbers x and y are such that x > y. If the difference of these numbers is 5 and their product is 24, find:
- Sum of these numbers
- Difference of their cubes
- Sum of their cubes.
The sum of two numbers is 9 and their product is 20. Find the sum of their (i) Squares (ii) Cubes.
If `"a" + (1)/"a" = "p"`; then show that `"a"^3 + (1)/"a"^3 = "p"("p"^2 - 3)`
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If 2a - 3b = 10 and ab = 16; find the value of 8a3 - 27b3.
Evaluate the following :
(5.45)3 + (3.55)3
