a^2+b^2=25, a+b= 7 then a-b=_____
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Answers
Answer:
EXPLANATION.
\sf \implies a + \dfrac{1}{a + 1} = b + \dfrac{1}{b - 1} - 2⟹a+
a+1
1
=b+
b−1
1
−2
\sf \implies a - b + 2 \ne 0⟹a−b+2
=0
As we know that,
We can write equation as,
\sf \implies a + \dfrac{1}{a + 1} = (b - 2 )+ \dfrac{1}{b - 1}⟹a+
a+1
1
=(b−2)+
b−1
1
\sf \implies a - (b - 2) = \dfrac{1}{b - 1} - \dfrac{1}{a + 1}⟹a−(b−2)=
b−1
1
−
a+1
1
\sf \implies a - b + 2 = \dfrac{(a + 1) - (b - 1)}{(b - 1)(a + 1)}⟹a−b+2=
(b−1)(a+1)
(a+1)−(b−1)
\sf \implies a - b + 2 = \dfrac{a + 1 - b + 1}{ab + b - a - 1}⟹a−b+2=
ab+b−a−1
a+1−b+1
\sf \implies a - b + 2 = \dfrac{a - b + 2}{ab - a + b - 1}⟹a−b+2=
ab−a+b−1
a−b+2
\sf \implies 1 = \dfrac{1}{ab - a + b - 1}⟹1=
ab−a+b−1
1
\sf \implies ab - a + b - 1 = 1⟹ab−a+b−1=1
\sf \implies ab - a + b = 1 + 1⟹ab−a+b=1+1
\sf \implies ab - a + b = 2⟹ab−a+b=2
Option [3] is correct answer.
Answer:
3 is correct answer 3 is the correct answer