Question

how many distinct real numbers belongs to the following collection {in(4 - √15) ; in ( 4 + √ 15) (4 - √15) ; ( 4 + √15) ; in (4+√15 /4 - √15 ) ; in ( 31 + 8√15 )}​

Answer 1

Step-by-step explanation:

In this question it is given that

{ln(2−3–√),ln(2+3–√),−ln(2−3–√),−ln(2+3–√),ln(2+3–√2−3–√),ln(7+43–√)}

We have to find the number of distinct real roots.

So, Case 1:

ln(2−3–√) . . . . (given)

On multiplying and dividing withOn multiplying and dividing with ln(2+3–√) we get,

ln(2−3–√)=ln(2−3–√)×2+3–√2+3–√

On simplifying the above equation, we get,

ln(2−3–√)=ln(2+3–√)−1

By using log(ln) properties we get,

ln(2−3–√)=−ln(2+3–√)

Case 2: