Advertisements
Advertisements
प्रश्न
If \[\frac{a}{b} + \frac{b}{a} = 1\] then a3 + b3 =
विकल्प
- 1
-1
- \[\frac{1}{2}\]
0
Advertisements
उत्तर
Given `a/b + b/a = 1`
`(a xx a)/(b xx a) +(b xx b) /(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)`we get,
`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^3 ` is 0 .
APPEARS IN
संबंधित प्रश्न
Evaluate the following product without multiplying directly:
104 × 96
Factorise the following using appropriate identity:
4y2 – 4y + 1
Verify:
x3 + y3 = (x + y) (x2 – xy + y2)
Write in the expanded form: (ab + bc + ca)2
Evaluate of the following:
(598)3
Find the following product:
\[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]
Find the following product:
If x = −2 and y = 1, by using an identity find the value of the following
If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz
If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]
If a1/3 + b1/3 + c1/3 = 0, then
Evalute : `((2x)/7 - (7y)/4)^2`
If a - b = 0.9 and ab = 0.36; find:
(i) a + b
(ii) a2 - b2.
Use the direct method to evaluate :
(ab+x2) (ab−x2)
Expand the following:
(a + 4) (a + 7)
Expand the following:
(x - 3y - 2z)2
If p + q = 8 and p - q = 4, find:
pq
If `"a" + (1)/"a" = 2`, then show that `"a"^2 + (1)/"a"^2 = "a"^3 + (1)/"a"^3 = "a"^4 + (1)/"a"^4`
Which one of the following is a polynomial?
