Homework Help

Suppose that a + b = 3 and a^2 + b^2 = 7. Then a^4 + b^4 is equal to(a) 45 (b) 47 (c)...

user profile pic

christiano-cr7 | (Level 1) Salutatorian

Posted September 23, 2013 at 10:38 AM via web

dislike 1 like

Suppose that a + b = 3 and a^2 + b^2 = 7. Then a^4 + b^4 is equal to
(a) 45

(b) 47

(c) 49

(d) 51

(e) 81

1 Answer | Add Yours

user profile pic

llltkl | College Teacher | (Level 3) Valedictorian

Posted September 23, 2013 at 10:53 AM (Answer #1)

dislike 3 like

Given `a + b = 3` and `a^2 + b^2 = 7` .

`a^2 + b^2=(a+b)^2-2ab`

` rArr 7=(3)^2-2ab`

`rArr 2ab=2`

`rArr ab=1`

Now, `a^4 + b^4=(a^2 + b^2)^2-2a^2b^2`

                    `=(a^2 + b^2)^2-2(ab)^2`

                     ` =(7)^2-2(1)^2`

                      `=49-2`

                      ` =47`

Therefore, the correct answer is option (b).

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes