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Question

If ab=23 then find the values of the following expressions.

1. 4a+3b3b

2.5a2+2b25a22b2

3.a3+b3b3

4.7b4a7b+4a

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Solution

ab=23

Let a=2k, b=3k

(A) 4a+3b3b=4(2k)+3(3k)3(3k)

=8k+9k9k=17k9k=179


(B) 5a2+2b25a22b2

=5(2k)2+2(3k)25(2k)22(3k)2=5(4k2)+2(9k2)5(4k2)2(9k2)

=20k2+18k220k218k2=38k22k2=19


(C) a3+b3b3=(ab)3+1

=1+827=27+827=3527


(D) 7b4a7b+4a=7(3k)4(2k)7(3k)+4(2k)

=21k8k21k+8k=13k29k=1329.

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