Question

a^2+b^2=2 then a+b lies in the interval

Answer 1

there is any options....?

Answer 2

all are closed intervals and the options are -1,1. -2,2. 1,2. -2,2

Answer 3

ans

Answer 4

i cant get this but similar to this i show one...

Answer 5

If a2 + b2 + c2 = 1, then bc + ca + ab lies in the interval
(a) [-1/2,3] (b) [-1,2] (c) [-1/2,1] (d) [-1,1/2]

Answer 6

Given, a2 + b2 + c2 = 1
We know that,
(a + b + c)2 ≥ 0
⇒ a2 + b2 + c2 + 2(ab + bc + ca) ≥ 0
⇒ 1 + 2(ab + bc + ca) ≥ 0
⇒ ab + bc + ca ≥
Again, (b - c)2 + (c - a)2 + (a - b)2 ≥ 0
⇒ 2(a2 + b2 + c2) - 2(ab + bc + ca) ≥ 0
⇒ ab + bc + ca ≤ a2 + b2 + c2
⇒ ab + bc + ca ≤ 1
Hence,