Question

(a^-8 b)^1/4×(ab^-6)^1/3

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Answer 1

Answer:

a + b = 6 …………….. (1)

ab = 8 …………………(2)

a = 6 - b ……………….(using 1)

Substituting ‘a’ in (2)

(6-b)b = 8

- b^2 + 6b = 8

- b^2 + 6b -8 = 0

b^2 - 6b + 8 = 0 …………………(taking (-1) common)

Method 1

b^2 - 2b - 4b + 8 = 0

b(b-2) - 4(b-2) = 0

(b-2)(b-4) = 0

b - 2 = 0

b = 2

a = 6 -2

a = 4

b - 4 = 0

b = 4

a = 6 - 4

a = 2

Method 2

If (ax^2 + bx + c =0) is a quadratic equation, then its roots can be found using discriminant method

D = b^2 - 4ac

x = {-b +_ sqrt (D)}/2a}

Equation = b^2 - 6b + 8

Here a = 1, b = -6, c = 8

D = (-6)^2 - 4(1)(8)

D = 36 - 32 = 4

For roots,

{6 +- sqrt(4)}/2(1)

= {6 +- 2)/2

(6 + 2)/2 = 8/2

b = 4 ……………………….. (Here b implies to the variable in equation)

(6 – 2)/2 = 4/2

b = 2 ……………………….. (Here b implies to the variable in equation)

For b = 4,

a = 6–4 =2

For b = 2,

a = 6–2 = 4

Step-by-step explanation:

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