Question

if a + b = root 5 and a - b= root 3 then the value of (a2 + b2)

Answer 1

Answer:

4

Step-by-step explanation:

Given :

a + b = √5

a - b = √3

Note that : a² + b²

= > a² + ab + b² + ab - 2 ab

= > ( a + b )² - 2 ab

= > ( a + b )² - 4 ab / 2

= > ( a + b )² - [ a² + b² + 2 ab + 2 ab - a² - b² ] / 2

= > ( a + b )² - [ ( a + b )² - ( a - b )² ] / 2

Now put the values & enjoy :

= > ( √5 )² - [ ( √5 )² - ( √3 )² ] / 2

= > 5 - [ 5 - 3 ] / 2

= > 5 - 2/2

= > 5 - 1

= > 4

Answer 2

Answer:

Step-by-step explanation:

|A|=2

|B|=5

|A×B|=8

We know that ,

|A×B|=|A||B|sinθ

So, 2×5×sinθ=8

⟹sinθ=45

⟹cosθ=35

To evaluate:

A⋅B=|A||B|cosθ

⟹A⋅B=2×5×35

⟹A⋅B=6