Question

A+b=9 and ab=20 then find a^3+b^3

Answer 1

Answer:

189

Step-by-step explanation:

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

putting the values given

9^3=a^3+b^3+3(20)(9)

729=a^3+b^3+540

a^3+b^3=729-540

=189

Answer 2

Step-by-step explanation:

$ab = 20 \\ a = \frac{20}{b}$

Now we put the value of a in a+b=9

$a + b = 9 \\ \frac{20}{b} + b = 9 \\ \frac{20 + {b}^{2} }{b} = 9 \\ 20 + {b}^{2} = 9b \\ {b}^{2} - 9b + 20 = 0 \\ {b}^{2} - 5b - 4b + 20 = 0 \\ b(b - 5) - 4(b - 5) = 0 \\ (b - 5)(b - 4) = 0$

b=5 or 4

Now we put b= 5 in a+b=9

a + b=9

a+5=9

a=9-5

a=4

Now we put b=4 in a+b=9

a+b=9

a+4=9

a=9-4

a=5

ATQ

Case 1 a=4 & b=5

${a}^{3} + b {}^{3} \\ 4 {}^{3} + {5}^{3} \\ 64 + 125 \\ 189$

Case 2 a=5 & b=4

Similarly , its answer will be 189