Mathematics
If a − b + c = 6 and a2 + b2 + c2 = 38, then ab + bc − ca is :
0
1
-1
not possible
Expansions
1 Like
Answer
Given,
a - b + c = 6
a2 + b2 + c2 = 38
We know that,
⇒ [(a - b) + (c)]2 = (a - b)2 + c2 + 2 × (a - b) × c
⇒ [(a - b) + (c)]2 = a2 + b2 - 2 × a × b + c2 + 2ac - 2bc
⇒ (6)2 = a2 + b2 + c2 - 2(ab - ac + bc)
⇒ 36 = 38 - 2(ab - ac + bc)
⇒ 2(ab + bc − ca) = 38 - 36
⇒ 2(ab + bc − ca) = 2
⇒ (ab + bc − ca) =
⇒ (ab + bc − ca) = 1.
Hence, Option 2 is the correct option.
Answered By
3 Likes
Related Questions
The value of ab if 3a + 5b = 15 and 9a2 + 25b2 = 75 is :
4
5
6
8
If l + m − n = 9 and l2 + m2 + n2 = 31, then mn + nl − lm is :
-25
25
-2
-5
Assertion (A): (26)3 + (−15)3 + (−11)3 = 3 × 26 × 15 × 11.
Reason (R): If x + y + z = 0, then x3 + y3 + z3 = 3xyz
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Assertion (A): If , then .
Reason (R): x2 - 2x - 1 can be written as (x - 1)2.A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false