Manipal MET2019MathematicsQuadratic Equation

The number of real solutions of the equation 1+ |e^x-1 |=e^x (e^x-2 ) is

Options

Correct answer

A. 1

Step-by-step solution

aligned & We have, 1+ |e^x-1 |=e^x (e^x-2 ) & 1+1+ |e^x-1 |=e^ 2 x -2 e^x+1 & = (e^x-1 )^2 aligned gathered 1+1+ |e^x-1 |= |e^x-1 |^2 gathered Let (e^x-1 )=y , then aligned & y^2-y-2=0 y=2,-1 & |e^x-1 |=2 e^x-1= 2 & e^x=1 2 e^x=3,-1 & or e^x=3 x= _e 3 aligned There is one real solution of the equation.

Practice Quadratic Equation on Quantrex Academy →

More from Quadratic Equation

If is the common root of the quadratic equations x^2-5 x+4 a=0 , x^2-2 a x-8=0 , where a R , then the value of ^4- ^3+68 is 2025 If , are the roots of x^2-5 x-6 =0 and , are the roots of x^2-5 x-6 =0 , then + + + = 2025 If , , are the roots of the equation x ^3+ px ^2+ qx + r =0 , then ( + )( + )( + )= 2025 Let f(x)=x^2+2 b x+2 c^2 and g(x)=-x^2-2 c x+b^2, x R . If b and c are nonzero real numbers such that f(x)> g(x) , then | c b | lies in the interval 2025 If x ^2-4 ax +5+ a >0 for all x R whenever a ( , ) , then 4 + = 2025 If , , are the roots of the equation x^3-12 x^2+k x-18=0 and one of them is thrice the sum of the other two roots, then ^2+ ^2+ ^2-k= 2025 The polynomial equation of degree 5 whose roots are the roots of the equation x^5-3 x^4-x^3+11 x^2-12 x+4=0 each increased by 2, is 2025 If the difference of the roots of the equation x^2-7 x+10=0 is same as the difference of the roots of the equation x ^2-17 x + k =0 , then a divisor of k is 2025 Full Quadratic Equation list All Manipal MET PYQs