Advertisements
Advertisements
Question
If 2x + 3y = 8 and xy = 2 find the value of `4x^2 + 9y^2`
Advertisements
Solution
`(2x + 3y)^2 = (2x)^2 + (3y)^2 + 2(2x)(3y)`
`=> (2x + 3y)^2 = 4x^2 - 9y^2 + 12xy`
`=> (8)^2 = (4x^2 + 9y^2 + 24)` [∵ 2x + 3y = 8, xy = 24]
`=> 64 - 24 = 4x^2 + 9y^2`
`=> 4x^2 + 9y^2 = 40`
APPEARS IN
RELATED QUESTIONS
Factorise the following using appropriate identity:
9x2 + 6xy + y2
Expand the following, using suitable identity:
(x + 2y + 4z)2
Write the following cube in expanded form:
`[x-2/3y]^3`
If \[x - \frac{1}{x} = 7\], find the value of \[x^3 - \frac{1}{x^3}\].
If \[x - \frac{1}{x} = 5\], find the value of \[x^3 - \frac{1}{x^3}\]
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
Find the following product:
(3x + 2y) (9x2 − 6xy + 4y2)
Find the following product:
\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]
Find the following product:
\[\left( \frac{3}{x} - \frac{5}{y} \right) \left( \frac{9}{x^2} + \frac{25}{y^2} + \frac{15}{xy} \right)\]
Find the following product:
Find the following product:
If \[x + \frac{1}{x}\] 4, then \[x^4 + \frac{1}{x^4} =\]
If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] =
Evaluate, using (a + b)(a - b)= a2 - b2.
15.9 x 16.1
The coefficient of x in the expansion of (x + 3)3 is ______.
Expand the following:
(–x + 2y – 3z)2
Factorise the following:
9x2 + 4y2 + 16z2 + 12xy – 16yz – 24xz
Factorise the following:
16x2 + 4y2 + 9z2 – 16xy – 12yz + 24xz
Without actually calculating the cubes, find the value of:
(0.2)3 – (0.3)3 + (0.1)3
