If a+b=4 and ab=4,show that a=b
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Solution: a+b=4 = a=4-b...1
ab=4....2
put the value of a in 2nd.
(4-b)b=4
or,. 4b- b^2=4
or,. b^2-4b+4=0
or,. b^2-2b-2b+4=0
or,. b(b-2)-2(b-2)=0
or,. (b-2)(b-2)=0
Now, (b-2)=0
b=2...(a)
put the value of b in 1.
a=4-2
or,. a=2...(b)
From (a)and(b),we get
a=b
…............................
ab=4....2
put the value of a in 2nd.
(4-b)b=4
or,. 4b- b^2=4
or,. b^2-4b+4=0
or,. b^2-2b-2b+4=0
or,. b(b-2)-2(b-2)=0
or,. (b-2)(b-2)=0
Now, (b-2)=0
b=2...(a)
put the value of b in 1.
a=4-2
or,. a=2...(b)
From (a)and(b),we get
a=b
…............................
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