Question

If a-b = 4 and ab = 45, find the value of a3 + b3

Answer 1

your answer is here... just check it is it correct or wrong.

Answer 2

Answer:

Step-by-step explanation:

Given: a-b=4 and ab=45

The value of $a^{3}+b^{3}$ is given by: $(a+b)(a^{2}+b^{2}-ab)$  (1)

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

Putting the values of a-b and ab, weget

$16=a^{2}+b^{2}-90$

$a^{2}+b^{2}=106$

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

$(a+b)^{2}=106+90$

$(a+b)^{2}=196$

$a+b=14$

Now, putting these values in (1), we get

$a^{3}+b^{3}$=$(14)(106-45)=854$