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
Without actually calculating the cubes, find the value of the following:
(28)3 + (–15)3 + (–13)3
Simplify the following:
322 x 322 - 2 x 322 x 22 + 22 x 22
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
If \[x - \frac{1}{x} = - 1\] find the value of \[x^2 + \frac{1}{x^2}\]
Evaluate of the following:
(9.9)3
If a + b = 8 and ab = 6, find the value of a3 + b3
If x = −2 and y = 1, by using an identity find the value of the following
Find the following product:
(4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx)
Mark the correct alternative in each of the following:
If \[x + \frac{1}{x} = 5\] then \[x^2 + \frac{1}{x^2} = \]
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
If a - `1/a`= 8 and a ≠ 0 find :
(i) `a + 1/a (ii) a^2 - 1/a^2`
Use the direct method to evaluate :
`("z"-2/3)("z"+2/3)`
Use the direct method to evaluate :
`("a"/2-"b"/3)("a"/2+"b"/3)`
Evaluate: (2 − z) (15 − z)
Find the squares of the following:
3p - 4q2
Simplify by using formula :
(a + b - c) (a - b + c)
If `"a" - 1/"a" = 10;` find `"a" + 1/"a"`
If `"a" - 1/"a" = 10`; find `"a"^2 - 1/"a"^2`
If x + y + z = 12 and xy + yz + zx = 27; find x2 + y2 + z2.
Without actually calculating the cubes, find the value of:
(0.2)3 – (0.3)3 + (0.1)3
