Question

if a^3+b^3=9 and a+b=3 find ab

Answer 1

Answer:

a^3+b^3=9

since,a+b=3

(cube both side)

(a+b)^3=(3)^3

a^3+b^3+3ab(a+b)=27

9+3ab*3=27                    [ a^3+b^3=9, a+b=3 ]

9+9ab=27

9(1+ab)=27

1+ab=27/9

1+ab=3

ab=3-1

ab=2

Answer 2

The given question is if

${a}^{3} + {b}^{3} = 9 \: \: and \: \: a + b = 3$

we have to find the value of ab.

This question is under algebra. The algebraic formulae for the cubic equation is

${ (a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b)$

The value of a+b is given as 3. which means the cube of a+b is 3 cube

${3}^{3} = 27$

The given values are

${a}^{3} + {b}^{3} = 9$

substituting the obtained value in the cubic formulae, we get the answer as

$9 + 3ab \times 3 = {3}^{3}$

$9 + 3ab \: \: \times 3 = 27$

on further proceeding, we get the answer as,

$9 + 9ab = 27$

Taking the value 9 as common

$9(1 + ab) = 27 \\ 1 + ab = \frac{27}{9} \\ 1 + ab = 3$

The value 1 on the left side moves on to the right side, and we get

$ab = 3 - 1 = 2$

The obtained value of an is 2.

The algebraic formulae for the quadratic equation is

${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$

Hence, there are various formulas for each equation in algebra

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