if a+b=a/b+b/athen find the value of a*a + b*bplease give the solution
Aurosmit sahoo , 7 Years ago
Grade 11
Algebra> if a+b=a/b+b/a then find the value of a*a...
2 AnswersAbhishek tripathi
Last Activity: 7 Years ago
We can write a*a=a^2, b*b=d^2Need to find (a^2+b^2)a + b = a/b + b/aThan, a + b = (a^2+b^2)/abThan, (a + b)/ab = a^2+b^2As per question a^2 + b^2 = (a + b)/abAns is (a + b)/ab
RAJIB NAHA
Last Activity: 6 Years ago
a
a + b = a/b + b/a
a2b + ab2 = a2 + b2
a2b – a2 + ab2 – b2 = 0
(b-1)a2 + b2a – b2 = 0
Determinant [D] = (b2)2 – 4.(b-1).(-b2) has to be greater than equal to ‘0’.
Thus (b2).[b2+ 4b – 4] >= 0
OR b2+ 4b – 4 >= 0
Thus (b2).[b2+ 4b – 4] >= 0
OR b2+ 4b – 4 >= 0
OR (b+2)2 – 8 >= 0
OR (b + 2)2 >= 8
For b to be an +ve integer, the first considerable value of (b + 2)2 should be 9
Thus b + 2 = 3
OR b = 1.
Putting value of b = 1, in the original equation we get
(1-1)a2 + 12.a – (1)2 = 0
OR a = 1;
Thus a2 + b2 = (1)2 + (1)2 = 1 + 1 = 2.
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