Advertisements
Advertisements
प्रश्न
If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 + c2.
Advertisements
उत्तर
Given, a + b + c = 9 and ab + bc + ca = 26 ...(i)
Now, a + b + c = 9
On squaring sides, we get
(a + b + c)2 = (9)2
⇒ a2 + b2 + c2 + 2ab + bc + ca = 81 ...[Using identity, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca]
⇒ a2 + b2 + c2(ab + bc + ca) = 81
⇒ a2 + b2 + c2 + 2(26) = 81 ...[From equation (i)]
⇒ a2 + b2 + c2 = 81 – 52 = 29
APPEARS IN
संबंधित प्रश्न
Factorise the following using appropriate identity:
4y2 – 4y + 1
Evaluate the following using suitable identity:
(998)3
Factorise the following:
27 – 125a3 – 135a + 225a2
Evaluate the following:
(98)3
Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
If a + b + c = 9 and ab + bc + ca =23, then a3 + b3 + c3 − 3abc =
The product (x2−1) (x4 + x2 + 1) is equal to
If a2 - 5a - 1 = 0 and a ≠ 0 ; find:
- `a - 1/a`
- `a + 1/a`
- `a^2 - 1/a^2`
Evaluate: (9 − y) (7 + y)
Evaluate: `(2"x"-3/5)(2"x"+3/5)`
Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`
Expand the following:
(a + 3b)2
Find the squares of the following:
9m - 2n
If x + y = 1 and xy = -12; find:
x - y
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a" + (1)/"a"`
Simplify:
`(x - 1/x)(x^2 + 1 + 1/x^2)`
Expand the following:
(–x + 2y – 3z)2
Factorise the following:
25x2 + 16y2 + 4z2 – 40xy + 16yz – 20xz
Find the following product:
`(x/2 + 2y)(x^2/4 - xy + 4y^2)`
Multiply x2 + 4y2 + z2 + 2xy + xz – 2yz by (–z + x – 2y).
