 Hello and welcome to the session. In this session, we discussed the following question which says, solve the following quadratic equation 5 to the power x plus 1 plus 5 to the power 1 minus x is equal to 10. We need to find the value of x for this quadratic equation. So let's proceed with the solution. The given quadratic equation is 5 to the power x plus 1 plus 5 to the power 1 minus x is equal to 10. So this means we get 5 to the power x into 5 to the power 1 plus 5 to the power 1 into 5 to the power minus x is equal to 10. That is we have 5 into 5 to the power x plus 5 upon 5 to the power x is equal to 10. Now we take let 5 to the power x be equal to y. So putting 5 to the power x equal to y in this equation we get 5 into y plus 5 upon y is equal to 10. So this means we get, now on the LHS we take the LCM so we get y in the denominator. In the numerator we have 5y multiplied by y plus 5 is equal to 10. This gives us 5y square plus 5 upon y is equal to 10. Further we have 5y square plus 5 is equal to 10y. Or we can say we get 5y square minus 10y plus 5 is equal to 0. We take 5 common on the LHS inside the bracket we have y square minus 2y plus 1 is equal to 0. Or you can say we get y square minus 2y plus 1 equal to 0. So we have got this quadratic equation. Now we will solve this quadratic equation for y. So we can split the middle term. That is we need to find two numbers such that their sum is the coefficient of y which is minus 2. And their product is this 1 that is the constant term multiplied by the coefficient of y square which is 1. So the two numbers that we obtain are minus 1 and minus 1. So we can write the middle term as minus y minus y. So we get the quadratic equation y square minus y minus y plus 1 is equal to 0. We make these pairs from the first pair we take out y common inside we have y minus 1. From the second pair we take out minus 1 common and inside the bracket we are left with y minus 1. This is equal to 0. This means we get y minus 1 into y minus 1 is equal to 0. Further we have y minus 1 whole square is equal to 0. Or we can say y minus 1 equal to 0 which gives us y is equal to 1. So we have got the value of y as 1 and we had assumed y to be 5 raised to the power x. So we now get 5 raised to the power x is equal to y which is 1. Now this means 5 raised to the power x is equal to 5 raised to the power 0. Since we know that any number raised to the power 0 is equal to 1. So this gives us x is equal to 0. So x equal to 0 is our final answer. This completes the session. Hope you have understood the solution for this question.