Question

if a+b = 6 and ab= 8 , evaluate (i) a2 +b2 and (ii) a-b

Answer 1

Answer:

a = 4 , B = 2

i) a² + b² = (4)² + (2)²

= 16 + 4 = 20

ii) a-b = 4-2

= 2

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Answer 2

Answer:

a² + b² = 20
a - b = 2

Step-by-step explanation:

Let a and b be  α and β respectively, which are the roots of a quadratic equation

It is given that,
a + b = 6

∴ α + β = 6   &

ab = 8

∴ αβ = 8

We know that,

α² + β² = (α + β)² - 2αβ

           = 6² - 2 x 8

           = 36 - 16

∴ α² + β² = 20

Now, we know

to for a quadratic equation from given roots,

x² - (α + β)x +  αβ = 0

∴ x² - 6x + 8 = 0

By factorization method,

x² - 4x - 2x + 8 = 0

x( x - 4) -2(x - 4) = 0

(x - 4) (x - 2) = 0

∴ x - 4 = 0 or x - 2 = 0

∴ x = 4 or x = 2

Thus, α = 4 and β = 2

∴ α - β = 4 - 2 = 2
∴ a - b = 2