Advertisements
Advertisements
Question
If a + b = 7 and ab = 12, find the value of a2 + b2
Advertisements
Solution
We have to find the value of `a^2 +b^2`
Given `a + b = 7 ,ab = 12`
Using identity `(a+b)^2 = a^2 + 2ab +b^2`
By substituting the value of a + b = 7 ,ab = 12we get
`(a+b)^2 = a^2 +b^2 + 2 xx ab`
`(7)^2 = a^2 +b^2 + 2 xx 12`
`49 = a^2 +b^2 + 24`
By transposing +24 to left hand side we get ,
`49 - 24 = a^2 +b^2`
`25 = a^2 +b^2`
Hence the value of `a^2 +b^2 ` is 25.
APPEARS IN
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
103 × 107
Evaluate the following product without multiplying directly:
104 × 96
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
Evaluate the following using identities:
(0.98)2
Simplify the following:
0.76 x 0.76 - 2 x 0.76 x 0.24 x 0.24 + 0.24
Simplify the following
`(7.83 + 7.83 - 1.17 xx 1.17)/6.66`
Simplify the following products:
`(m + n/7)^3 (m - n/7)`
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
Evaluate of the following:
(9.9)3
(x − y) (x + y) (x2 + y2) (x4 + y4) is equal to ______.
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
Use the direct method to evaluate the following products:
(5a + 16) (3a – 7)
Simplify by using formula :
(5x - 9) (5x + 9)
Simplify by using formula :
(1 + a) (1 - a) (1 + a2)
If x + y = 9, xy = 20
find: x2 - y2.
If `x + (1)/x = 3`; find `x^2 + (1)/x^2`
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a" + (1)/"a"`
Evaluate the following :
7.16 x 7.16 + 2.16 x 7.16 + 2.16 x 2.16
The value of 2492 – 2482 is ______.
