#MathUnusual | Solve for n? Only Genius can solve !!!!

Hello friends, this is Mahesh Ivlekar and you are watching NextGenMaths. Example, cube root n plus square root n square plus 8 plus cube root n minus square root n square plus 8 equal to 8. For which values of n it is true? If you want to solve then stop the video, otherwise let's start the solution. Say cube root n plus square root n square plus 8 equal to a and cube root n minus square root n square plus 8 equal to b then equation become a plus b equal to 8. Now we are going to calculate a into b. So both are the cube root to take under the single cube root then these are the x plus y x minus y factor then factor formula x square minus y square so square of n square minus square of square root n square plus 8. Now square root cancel the square we have n square minus n square plus 8 so n square minus n square cancel we have only cube root minus 8 and cube root is minus 2 so a into b is equal to minus 2. Now using this two value a plus b and a b we are going to find the value of a minus b which is square root a plus b whole square minus 4 a b substitute the value of a b and a plus b 8 and minus 2 then we have 64 plus 8 that is square root 72 if we simplify 36 into 2 so it is 6 into root 2 so a minus b is equal to 6 into root 2. Now take the sum of this two equation a plus b a minus b then we have b b cancel 2 a equal to 8 plus 6 root 2 so divide by 2 the equation then we have a equal to 4 plus 3 root 2 but a equal to cube root n plus square root n square plus 8 substitute then the equation is cube root n plus square root n square plus 8 equal to 4 plus 3 root 2. By taking cube on the both side we have n plus square root n square plus 8 equal to 4 plus 3 root 2 power 3. Now apply the cubic formula this is cube of first term plus cube of second term plus three times first term into square of second term plus three times square of first term into second term. Now cube of 4 is 64 and this simplify all the numbers then we have 64 plus 54 root 2 plus 216 plus 144 root 2. Now add this two terms terms of root 2 and the terms of natural numbers then we have 280 plus 192. If we rewrite it will become a square root of 280 square plus 8. Now if we compare then n equal to 280. This equation will have the solution n equal to 280. Thanks for watching for more videos like, share, subscribe, press the bell icon of next channel.