Question

If a+b=1
and a ² + b sq. = 2
acube + bcube =__________​

Answer 1

Answer:

5/2

Step-by-step explanation:

a+b=1-------(1)

squaring both side

(a+b)²=1²

a²+b²+2ab=1

a²+b²=1-2ab------(2)

a²+b²=2(given)----------(3)

from (2) and (3)

1-2ab=2

-1=2ab

$\frac{-1}{2} =ab$---------(4)

a³+b³=(a+b)(a²+b²-ab)       {substituting the values}

⇒(1)[2-(-1/2)]

⇒2+1/2

⇒5/2

Answer 2

$a + b = 1$

Squaring Both Sides,

${a}^{2} + {b}^{2} + 2ab = 1$

Putting the Given Value, $a^2 + b^2 = 2$

$2 + 2ab = 1 \\ 2ab = - 1 \\ ab = - \dfrac{ 1}{2}$

To Find:

${a}^{3} + {b}^{3} \\ = (a + b)( {a}^{2} + {b}^{2} - ab) \\ = (1)(2 - ( - \dfrac{1}{2} )) \\ = (1)(2 + \frac{1}{2} ) \\ = \frac{5}{2}$