Question

The roots of the equation (2x - 7)(x2 - 9) (2x + 5) = 91 is -​

Answer 1

Answer:

(2x-7).(x+3).(x-3).(2x+5) = 91.

Multiply the first two expressions and then the next two expressions, we get,

(2x2−x−21).(2x2−x−15)=91 .

In the above, take t=2x2−x

So, we have (t-21).(t-15) = 91

t2−36t+315=91 .

or, t2−36t+224=0

or, t2−28t−8t+224=0

or, t.(t−28)−8.(t−28)=0

or, (t−8)(t−28)=0 .

2x2−x=8 or 28

If RHS = 8.

2x2−x−8=0 .

solving for x=+1±1+64√4

so x=1±65√4

If RHS = 28.

2x2−x=28

or 2x2−x−28=0

or 2x2−8x+7x−28=0

or, (x−4).(2x+7)=0.

So, solution set x∈{4,−72,1+65√4,1−65√4}