JEE Main202522 Jan 2025Morning ShiftMathematicsBasics of MathematicsActual
The product of all solutions of the equation e ^ 5 ( _ e x )^2+3 =x^8, x 0 , is :
Options
- Ae^ 8 / 5
- Be^ 6 / 5
- Ce ^2
- De
Correct answer
A. e^ 8 / 5
Step-by-step solution
aligned & e ^ 5( x)^2+3 = x ^8 & ne ^ 5( x)^2+3 = nn ^8 & 5( x )^2+3=8 nx & ( nx = t ) & 5 t ^2-8 t +3=0 & t ₁+ t ₂= 8 5 & x ₁ x ₂= 8 5 & x ₁ X ₂= e ^ 8 / 5 aligned