Question

2a^2=5a-3 , 2b^2=5b-3 , (a^2+b^2)=?​

Answer 1

Step-by-step explanation:

a^2 = 5a-3. or, a^2-5a+3 =0 …………………..(1).

b^2 = 5.b -3. or, b^2 -5b+3 = 0.……….……….(2).

Thus, a and b are the roots of quadratic equation x^2 -5.x +3 =0.

Sum of the roots = a + b = -(-5)/1. = 5. or, a+ b =5. ………….(3).

Product of the roots = a.b = +(+3)/1= 3. or, a.b = 3. .………..(4).

Now , the sum of the given roots = a/b+b/a = (a^2+b^2)/a.b ,

= {(a+b)^2 -2.a.b}/a.b = {25–6}/3 = 19/3.

Product of the roots = (a/b)×(b/a)= 1.

Required equation is:-

x^2 - (sum of roots).x + product of the roots = 0.

or, x^2 - (19/3).x + 1 = 0.

or, 3.x^2 - 19.x + 3 = 0. Answer.