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Question

If a+b=1 and ab=7 ;

Find

(i) (a2+b2) (ii) ab


A

3

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B

2

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C

(i) 26 (ii) -13

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D

(i) -25 (ii) 12

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Solution

The correct option is A

3


(i) Given that a + b = 1 and (a- b) = 7

Squaring (a+b) , we get

(a+b)2 = a2+2ab+b2
(1)2 = a2+2ab+b2
1=(a2+2ab+b2) ----------------------------(1)

Similarly Squaring (a-b) , we get
(ab)2 = a22ab+b2
(7)2 = a22ab+b2
49=(a22ab+b2) ----------------------------------(2)

Adding (1) and (2) , we get

1=(a2+2ab+b2)
+ 49=(a22ab+b2)
____________________________
50=2(a2+b2)
25=(a2+b2)

(ii) We know 25=(a2+b2)

Substituting in 1st equation , we get

1=(25+2ab)
24=2ab
ab=12


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