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

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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).**

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