Question

A is equal to 1 minus root 7 by 1 + root 7 and b is equal to 1 + root 7 by 1 minus root 7 value of a square + a b + b square by a square minus a b + b square

Answer 1

HEY MATE HERE IS THE ANSWER TO YOUR QUESTION --

A² + B² = 7 [eqn 1]

A³ + B³ = 10 [eqn 2]

Using Identities

(A+B)² = A² + B² + 2AB [eqn 3]

and

(A+B)³ = A³ + B³ + 3AB(A+B) [eqn 4]

Put [eqn 1] in [eqn 3] and

[eqn 2] in [eqn 4]

(A+B)² = 7 + 2AB [eqn 5]

(A+B)³ = 10 + 3AB(A+B) [eqn 6]

Make AB the subject of the formula in [eqn 5] and [eqn 6]

AB = [(A+B)² - 7]÷2 [eqn 7] from[eqn 5]

AB = [(A+B)³ - 10]÷[3(A+B)] [eqn 8] from [eqn 6]

Compare the two equations.

[(A+B)² - 7]÷2 = [(A+B)³ - 10]÷[3(A+B)]

[3(A+B)][(A+B)² - 7] = 2[(A+B)³ - 10]

Let A+B = c

3c(c²-7) = 2(c³-10)

3c³-21c = 2c³-20

c³ -21c + 20 = 0

(c+5)(c-4)(c-1) = 0

• c = A + B = -5, 4, 1

When A+B = -5

AB = [(-5)²-7]÷2 = 9 [using eqn 7]

Solving

A+B = -5

and

AB = 9

simultaneously,

Let i = √-1

A = -2.5 + (√11÷2)i or -2.5 - (√11÷2)i

B = -2.5 - (√11÷2)i or -2.5 + (√11÷2)i

When A+B = 4

AB = [(4)³ -10]÷[3(4)] = 4.5 [using eqn 8]

Solving

A+B = 4

and

AB = 4.5

simultaneously,

Let i = √-1

A = 2 + (√2÷2)i or 2 - (√2÷2)i

B = 2 - (√2÷2)i or 2 + (√2÷2)i

When A+B = 1

AB = [(1) - 7]÷2 = -3 [using eqn 7]

Solving

A+B =1

and

AB =3

simultaneously,

A = 0.5 + (√13÷2) or 0.5 - (√13÷2)

B = 0.5 - (√13÷2) or 0.5 - (√13÷2)

I HOPE IT HELPED YOU♥️

Answer 2

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