Advertisements
Advertisements
प्रश्न
Find the value of 4x2 + y2 + 25z2 + 4xy − 10yz − 20zx when x = 4, y = 3 and z = 2.
Advertisements
उत्तर
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
संबंधित प्रश्न
Verify:
x3 – y3 = (x – y) (x2 + xy + y2)
Factorise the following:
27y3 + 125z3
Without actually calculating the cubes, find the value of the following:
(28)3 + (–15)3 + (–13)3
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
Evaluate the following using identities:
(1.5x2 − 0.3y2) (1.5x2 + 0.3y2)
If `x + 1/x = sqrt5`, find the value of `x^2 + 1/x^2` and `x^4 + 1/x^4`
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
Write in the expanded form:
`(m + 2n - 5p)^2`
Simplify (2x + p - c)2 - (2x - p + c)2
Evaluate of the following:
(598)3
If `x^4 + 1/x^4 = 194, "find" x^3 + 1/x^3`
If x = −2 and y = 1, by using an identity find the value of the following
75 × 75 + 2 × 75 × 25 + 25 × 25 is equal to
Use identities to evaluate : (998)2
Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`
Evaluate: `(2"a"+1/"2a")(2"a"-1/"2a")`
Expand the following:
(2p - 3q)2
If `x + (1)/x = "p", x - (1)/x = "q"`; find the relation between p and q.
Expand the following:
`(4 - 1/(3x))^3`
