Question

Let a,b,be real numbers such that a+b = 1 and asq. + bsq. = 4 . Find the value of asq./2+b + bsq./2+a.​

Answer 1

Answer:

(a²/2) + b + (b²/2) + a = 3

Step-by-step explanation:

We have,

a + b = 1 ----- 1

a² + b² = 4

Now,

a² + b² = 4

Dividing both sides by 2, we get,

(a² + b²)/2 = 4/2

(a²/2) + (b²/2) = 2 ----- 2

Then, we have to find,

(a²/2) + b + (b²/2) + a = ?

Now, let's just rearrange,

(a²/2) + b + (b²/2) + a

Since,

Addition is Associative,

[(a²/2) + (b²/2)] + [a + b]

From eq.1 and eq.2 we get,

[2] + [1]

= 3

Hence,

(a²/2) + b + (b²/2) + a = 3

Hope it helped and believing you understood it....All the best