Advertisements
Advertisements
Question
Find the value of 4x2 + y2 + 25z2 + 4xy − 10yz − 20zx when x = 4, y = 3 and z = 2.
Advertisements
Solution
We have,
`4x^2 + y^2 + 25z^2 + 4xy - 10yz - 20zx`
`=> (2x)^2 + (y)^2 + (-5z)^2 + 2(2x)(y) + 2(y)(-5z) + 2(-5z)(2x)`
`=:> (2x + y - 5z)^2`
`=> [2[4] + 3 - 5(2)]^2` [∵ x = 4, y = 3 and z = 2]
`= [8 + 3 - 10]^2`
`=[1]^2`
= 1
`∴ 4x^2 + y^2 + 25z^2 + 4xy - 10yz - 20zx = 1`
APPEARS IN
RELATED QUESTIONS
Factorise the following using appropriate identity:
9x2 + 6xy + y2
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
Simplify the following:
0.76 x 0.76 - 2 x 0.76 x 0.24 x 0.24 + 0.24
Write in the expanded form:
`(a + 2b + c)^2`
Write in the expanded form (a2 + b2 + c2 )2
Simplify `(x^2 + y^2 - z)^2 - (x^2 - y^2 + z^2)^2`
Simplify (2x + p - c)2 - (2x - p + c)2
If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3
If a + b + c = 0, then write the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\]
If \[x^3 - \frac{1}{x^3} = 14\],then \[x - \frac{1}{x} =\]
Evaluate `(a/[2b] + [2b]/a )^2 - ( a/[2b] - [2b]/a)^2 - 4`.
If a - b = 7 and ab = 18; find a + b.
If a - b = 4 and a + b = 6; find
(i) a2 + b2
(ii) ab
Evaluate: (6 − 5xy) (6 + 5xy)
Find the squares of the following:
3p - 4q2
If `x + (1)/x = 3`; find `x^2 + (1)/x^2`
If a2 + b2 + c2 = 41 and a + b + c = 9; find ab + bc + ca.
If `"r" - (1)/"r" = 4`; find : `"r"^4 + (1)/"r"^4`
Simplify:
(3a + 2b - c)(9a2 + 4b2 + c2 - 6ab + 2bc +3ca)
Which one of the following is a polynomial?
