Question

if 3a²=6a-5 and 3b²=6b-5 then find the value of a+b where a not equal to b​

Answer 1

The value of a + b = 2

Given :

3a² = 6a - 5 and 3b² = 6b - 5

To find :

The value of a + b where a ≠ b

Solution :

Step 1 of 2 :

Write down the given equations

Here the given equations are

3a² = 6a - 5 and 3b² = 6b - 5

Step 2 of 2 :

Find the value of a + b

3a² = 6a - 5 and 3b² = 6b - 5

So a and b are two roots of the quadratic equation 3x² = 6x - 5

So the quadratic equation is

3x² = 6x - 5

⇒ 3x² - 6x + 5 = 0

Comparing the given polynomial with general quadratic equation Ax² + Bx + C = 0 we get

A = 3 , B = - 6 , C = 5

Sum of the roots

= a + b

$\displaystyle \sf{ = - \frac{B}{A } }$

$\displaystyle \sf = - \frac{ - 6}{3}$

$\displaystyle \sf = 2$

Product of the roots

$\displaystyle \sf{ = \frac{C}{A} }$

$\displaystyle \sf{ = \frac{5}{3} }$

Hence the required value of a + b = 2

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