Advertisements
Advertisements
प्रश्न
Evaluate:
483 − 303 − 183
Advertisements
उत्तर
Given 483 − 303 − 183
We shall use the identity `a^3 + b^3 + c^3 - 3abc = (a+b+c) (a^2 +b^2 + c^2 - ab - bc+ ca)`
Let Take a= 48 , b = 30,c =-18
`a^3 + b^3 +c^3 - 3abc = (a+b+c)(a^2 +b^2 + c^2 - ab - ab - ca)`
`a^3 + b^3 +c^3 = (a+b+c)(a^2 +b^2 + c^2 - ab - ab - ca) + 3abc`
`a^3 + b^3 +c^3 - 3abc = (48+30+18)(a^2 +b^2 + c^2 - ab - ab - ca)+3abc`
`a^3 + b^3 +c^3 = 0 xx (a^2 +b^2 + c^2 - ab - ab - ca) + 3abc`
`a^3 + b^3 +c^3 = + 3abc`
`48^3 - 30^3 - 18^3 = 3xx 48 xx -30 xx -18`
= 77760
Hence the value of `25^3 - 75^3 + 50^3`is 77760.
APPEARS IN
संबंधित प्रश्न
Evaluate the following product without multiplying directly:
104 × 96
Verify:
x3 + y3 = (x + y) (x2 – xy + y2)
Evaluate the following using identities:
(0.98)2
If 2x + 3y = 8 and xy = 2 find the value of `4x^2 + 9y^2`
Write in the expanded form:
`(a + 2b + c)^2`
If a + b = 10 and ab = 21, find the value of a3 + b3
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]
If \[a^2 + \frac{1}{a^2} = 102\] , find the value of \[a - \frac{1}{a}\].
Mark the correct alternative in each of the following:
If \[x + \frac{1}{x} = 5\] then \[x^2 + \frac{1}{x^2} = \]
If \[x^2 + \frac{1}{x^2} = 102\], then \[x - \frac{1}{x}\] =
Use the direct method to evaluate the following products:
(x + 8)(x + 3)
Use the direct method to evaluate :
(2+a) (2−a)
Evaluate: (5xy − 7) (7xy + 9)
Find the squares of the following:
(2a + 3b - 4c)
If `"a" + 1/"a" = 6;`find `"a" - 1/"a"`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
If a + b + c = 0, then a3 + b3 + c3 is equal to ______.
Expand the following:
(4a – b + 2c)2
Factorise the following:
9x2 + 4y2 + 16z2 + 12xy – 16yz – 24xz
Simplify (2x – 5y)3 – (2x + 5y)3.
