Advertisements
Advertisements
Question
If 9x2 + 25y2 = 181 and xy = −6, find the value of 3x + 5y
Advertisements
Solution
We have,
`(3x + 5y)^2 = (3x)^2 + (5y)^2 + 2 xx 3x xx 5y`
`=> (3x + 5y)^2 = 9x^2 + 25y^2 + 30xy`
`= 181 + 30(-6)` [∵ `9x^2 + 25y^2 = 181` and xy = -6]
= 181 - 180
`=> (3x + 5y)^2 = 1`
`=> (3x + 5y)^2 = (-+1)^2`
`=> 3x + 5y = +-1`
APPEARS IN
RELATED QUESTIONS
Use suitable identity to find the following product:
(x + 4) (x + 10)
Evaluate the following using identities:
`(2x+ 1/x)^2`
Evaluate the following using identities:
(2x + y) (2x − y)
Simplify the following
`(7.83 + 7.83 - 1.17 xx 1.17)/6.66`
Simplify the expression:
`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`
Evaluate of the following:
(9.9)3
Evaluate of the following:
`(10.4)^3`
If `x - 1/x = 3 + 2sqrt2`, find the value of `x^3 - 1/x^3`
Simplify of the following:
Find the following product:
(4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx)
Mark the correct alternative in each of the following:
If \[x + \frac{1}{x} = 5\] then \[x^2 + \frac{1}{x^2} = \]
If a − b = −8 and ab = −12, then a3 − b3 =
\[\frac{( a^2 - b^2 )^3 + ( b^2 - c^2 )^3 + ( c^2 - a^2 )^3}{(a - b )^3 + (b - c )^3 + (c - a )^3} =\]
Evalute : `( 7/8x + 4/5y)^2`
Use the direct method to evaluate :
(xy+4) (xy−4)
Use the direct method to evaluate :
(0.5−2a) (0.5+2a)
Evaluate, using (a + b)(a - b)= a2 - b2.
999 x 1001
If 2x + 3y = 10 and xy = 5; find the value of 4x2 + 9y2
If `"a" + (1)/"a" = 2`, then show that `"a"^2 + (1)/"a"^2 = "a"^3 + (1)/"a"^3 = "a"^4 + (1)/"a"^4`
