 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that solve for x, x raised to the power 4 plus x square is equal to 6. We know that x square minus y square can be written as x plus y the whole into x minus y the whole. Similarly, we can also factorize the quadratic expression of the type x square plus y square into complex linear factors using the result that is x square plus y square is equal to x plus iota y the whole into x minus iota y the whole. With this key idea let us proceed to the solution. We have to solve this equation that is x raised to the power 4 plus x square is equal to 6 and we can write this equation as x raised to the power 4 plus x square minus of 6 is equal to 0. Now let us assume x square is equal to y then this polynomial will get reduced to y square plus y minus of 6 is equal to 0 which is a quadratic equation in y. Now let us factorize this equation. So now we write y square this y can be written as plus 3y minus 2y minus of 6 is equal to 0. Here we are factorizing this polynomial expression using middle term splitting. This implies that now we can take y common from first two terms and we get y into y plus 3 the whole and here we can take minus 2 common from last two terms and we get minus 2 into y plus 3 the whole which is equal to 0. This further implies that now again taking y plus 3 common from these two terms we get y plus 3 the whole into y minus 2 the whole which is equal to 0. We had put the value of x square as y so now again putting in the value of y back to x square we get x square plus 3 the whole into x square minus 2 the whole is equal to 0. Now x square plus 3 can be written as x square plus square root of 3 whole square which is of the form x square plus y square also x square minus 2 can be written as x square minus of square root of 2 whole square which is of the form x square minus y square. Now this can be written as x square plus square root of 3 whole square the whole into x square minus square root of 2 whole square the whole is equal to 0. Now this expression is of the form x square plus y square and this expression is of the form x square minus y square and from the key idea we know that x square minus y square is equal to x plus y the whole into x minus y the whole and x square plus y square is equal to x plus iota y the whole into x minus iota y the whole. So using the key idea we get the factors as x plus square root of 3 iota the whole into x minus square root of 3 iota the whole into x plus square root of 2 the whole into x minus square root of 2 the whole which is equal to 0 which implies that x plus square root of 3 iota is equal to 0 or x minus square root of 3 iota is equal to 0 or x plus square root of 2 is equal to 0 or x minus square root of 2 is equal to 0. Thus we get the value of x as minus of square root of 3 iota square root of 3 iota minus of square root of 2 and square root of 2 which is the required answer. This completes our session hope you enjoyed this session.