Advertisements
Advertisements
Question
Using suitable identity, evaluate the following:
9992
Advertisements
Solution
9992 = (1000 – 1)2
= (1000)2 + (1)2 – 2 × 1000 × 1 ...[Using identity, (a – b)2 = a2 + b2 – 2ab]
= 1000000 + 1 – 2000
= 998001
APPEARS IN
RELATED QUESTIONS
Write the following cube in expanded form:
`[3/2x+1]^3`
Factorise the following:
27 – 125a3 – 135a + 225a2
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 3x2 – 12x |
Evaluate the following using identities:
`(2x+ 1/x)^2`
Evaluate the following using identities:
(0.98)2
Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2
Evaluate of the following:
1113 − 893
Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
If `x - 1/x = 3 + 2sqrt2`, find the value of `x^3 - 1/x^3`
Find the following product:
(4x − 5y) (16x2 + 20xy + 25y2)
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
(a − b)3 + (b − c)3 + (c − a)3 =
Find the square of `(3a)/(2b) - (2b)/(3a)`.
If a2 - 5a - 1 = 0 and a ≠ 0 ; find:
- `a - 1/a`
- `a + 1/a`
- `a^2 - 1/a^2`
If p + q = 8 and p - q = 4, find:
p2 + q2
If a2 + b2 + c2 = 41 and a + b + c = 9; find ab + bc + ca.
Simplify:
`(x - 1/x)(x^2 + 1 + 1/x^2)`
Find the following product:
(x2 – 1)(x4 + x2 + 1)
Without actually calculating the cubes, find the value of:
`(1/2)^3 + (1/3)^3 - (5/6)^3`
