Question

x^2-2ax+a^2=0×2-2ax+a2=0 find value of \{x}{a}ax​

Answer 1

x

2

−2ax+a

2

+a−3=0…(1)

⇒(x−a)

2

=3−a

Since, (x−a)

2

≥0

⇒3−a≥0

⇒a≤3

We have a formula for solving quadratic equation ax

2

+bx+c=0 is

x=

2a

−b±

b

2

−4ac

Now, the roots of equation (1) are

x=

2.1

−(−2a)±

(−2a)

2

−4.1.(a

2

+a−3)

x=a±

3−a

Since, roots are less than 3.

a+

3−a

<3

⇒

3−a

<3−a

⇒3−a<9+a

2

−6a

⇒a

2

−5a+6>0

⇒(a−2)(a−3)>0

⇒a<2 or a>3

Hence, a<2.