Advertisements
Advertisements
प्रश्न
If \[\frac{a}{b} + \frac{b}{a} = - 1\] then a3 − b3 =
पर्याय
1
-1
- \[\frac{1}{2}\]
0
उत्तर
Given `a/b+b/a = -1`
Taking Least common multiple in `a/b +b/a = -1 `we get,
` a/b + b/a -1`
`(axx a)/(b xx a)+(bxxb)/(a xx b) = -1`
`a^2/(ab) + b^2/(ab) = -1`
`(a^2 + b^2)/(ab) = -1 `
`a^2+b^2 = -1 xx ab`
`a^2 +b^2 = -ab`
`a^2 + b^2 + ab = 0`
Using identity `a^3 - b^3= (a-b) (a^2 +ab +b^2)`
`a^3 -b^3 = (a-b)(a^2 + ab+b^2)`
`a^3 -b^3 = (a-b)(0)`
`a^3 - b^3 = 0`
Hence the value of `a^3 - b^2` is 0.
APPEARS IN
संबंधित प्रश्न
Without actually calculating the cubes, find the value of the following:
(28)3 + (–15)3 + (–13)3
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 3x2 – 12x |
Evaluate the following using identities:
(1.5x2 − 0.3y2) (1.5x2 + 0.3y2)
Simplify the following products:
`(m + n/7)^3 (m - n/7)`
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
Write in the expanded form: (ab + bc + ca)2
Find the following product:
If a + b + c = 9 and a2+ b2 + c2 =35, find the value of a3 + b3 + c3 −3abc
If a + b = 7 and ab = 12, find the value of a2 + b2
If \[a^2 + \frac{1}{a^2} = 102\] , find the value of \[a - \frac{1}{a}\].
Evaluate : (4a +3b)2 - (4a - 3b)2 + 48ab.
If x + y = `7/2 "and xy" =5/2`; find: x - y and x2 - y2
Use the direct method to evaluate :
(3b−1) (3b+1)
Simplify by using formula :
(1 + a) (1 - a) (1 + a2)
If 2x + 3y = 10 and xy = 5; find the value of 4x2 + 9y2
If x + y + z = p and xy + yz + zx = q; find x2 + y2 + z2.
If `"r" - (1)/"r" = 4`; find: `"r"^2 + (1)/"r"^2`
Simplify:
`("a" - 1/"a")^2 + ("a" + 1/"a")^2`
Which one of the following is a polynomial?
Find the following product:
(x2 – 1)(x4 + x2 + 1)
