Advertisements
Advertisements
प्रश्न
Evaluate of the following:
1113 − 893
Advertisements
उत्तर
In the given problem, we have to find the value of numbers
Given 1113 − 893
We can write 1113 − 893 as `(100+ 11)^3 - (100 - 11)^3`
We shall use the identity `(a+b)^3 - (a-b)^3 = 2[b^3 + 3a^2b]`
Here a=100 , b = 11
\[{111}^3 - {89}^3 = \left( 100 + 11 \right)^3 - \left( 100 - 11 \right)^3\]
`= 2[11^3 + 3 (100)^2(11)]`
`= 2 [1331 + 330000]`
`= 2 [331331]`
` = 662662`
Hence the value of 1113 − 893 is 662662 .
APPEARS IN
संबंधित प्रश्न
Use suitable identity to find the following product:
(3 – 2x) (3 + 2x)
Factorise the following:
`27p^3-1/216-9/2p^2+1/4p`
Evaluate the following using identities:
117 x 83
If `x + 1/x = sqrt5`, find the value of `x^2 + 1/x^2` and `x^4 + 1/x^4`
Simplify the following products:
`(x/2 - 2/5)(2/5 - x/2) - x^2 + 2x`
If \[x - \frac{1}{x} = - 1\] find the value of \[x^2 + \frac{1}{x^2}\]
If \[x + \frac{1}{x} = 5\], find the value of \[x^3 + \frac{1}{x^3}\]
Find the following product:
\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]
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 a + b = 10 and ab = 16, find the value of a2 − ab + b2 and a2 + ab + b2
75 × 75 + 2 × 75 × 25 + 25 × 25 is equal to
If x + y = `7/2 "and xy" =5/2`; find: x - y and x2 - y2
Expand the following:
(a + 3b)2
Expand the following:
(x - 3y - 2z)2
Find the squares of the following:
3p - 4q2
If a - b = 10 and ab = 11; find a + b.
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
If `"r" - (1)/"r" = 4`; find: `"r"^2 + (1)/"r"^2`
Simplify:
(7a +5b)2 - (7a - 5b)2
