Advertisements
Advertisements
प्रश्न
Evaluate the following using identities:
117 x 83
Advertisements
उत्तर
The given expression is 117 x 83
We have
`(117 + 83)/2 = 200/2`
= 100
So we can express 117 and 83 in the terms of 100 as
117 = 100 + 17
83 = 100 - 17
117 x 83 = (100 + 17)(100 - 17)
We shall use the identity `(x - y)(x + y) = x^2 - y^2`
Here
(x + y) = 100 + 17
(x - y) = 100 - 17
By applying in identity we get
`(100 + 17)(100 - 17) = (100)^2 - (17)^2`
= 10000 - 289
= 9711
Hence the value of 1117 x 83 is 9711
APPEARS IN
संबंधित प्रश्न
Evaluate the following product without multiplying directly:
103 × 107
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
If 9x2 + 25y2 = 181 and xy = −6, find the value of 3x + 5y
Simplify (2x + p - c)2 - (2x - p + c)2
Find the value of 4x2 + y2 + 25z2 + 4xy − 10yz − 20zx when x = 4, y = 3 and z = 2.
If \[x^2 + \frac{1}{x^2} = 98\] ,find the value of \[x^3 + \frac{1}{x^3}\]
Evaluate of the following:
`(10.4)^3`
Evaluate of the following:
(598)3
Find the following product:
(4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx)
Evaluate:
483 − 303 − 183
If a1/3 + b1/3 + c1/3 = 0, then
Use the direct method to evaluate :
(x+1) (x−1)
Evaluate the following without multiplying:
(95)2
Evaluate the following without multiplying:
(103)2
If `"p" + (1)/"p" = 6`; find : `"p"^4 + (1)/"p"^4`
If `x + (1)/x = "p", x - (1)/x = "q"`; find the relation between p and q.
Simplify:
(3a - 7b + 3)(3a - 7b + 5)
If `49x^2 - b = (7x + 1/2)(7x - 1/2)`, then the value of b is ______.
Expand the following:
(3a – 5b – c)2
