Which equation has solutions of 6 and -6? x2 – 12x + 36 = 0 x2 + 12x – 36 = 0 x2 + 36 = 0 x2 – 36 = 0

Answer:The equation that has solutions 6 and -6 is [tex]x^2 - 36 = 0[/tex]Solution:We have to find which equation has the solutions 6 and -6. We have been given three equations. [tex]x^{2}-12 x+36=0[/tex]  --- eqn 1[tex]x^{2}+12 x-36=0[/tex] -- eqn 2[tex]x^{2}-36=0[/tex]  ---- eqn 3The 6 and -6 to satisfy any of these equations they have to be the roots of the equation. This means that when we substitute 6 and -6 in any of the equations and then solve them the answer on simplification should be 0. This condition should individually be satisfied by both 6 and -6 for any one of the equations. Now let us try and substitute 6 and -6 in eq1. Now, substituting 6 in eq1. 62-12×6+36=0 Now we simply the equation to check is the LHS is equal to the RHS of the equation.  LHS: 72-72=0 RHS:  0  Since LHS=RHS it is the root of the equation. Now we check if -6 satisfies eq1. -62-12×-6+36=0 LHS: 72+72=144 RHS:  0 Hence LHS is not equal to RHS, -6 is not the root of eq1. Similarly we check for eq2  Checking for 6 and -6 we get LHS is not equal to RHS hence this does not satisfy eq2. Now in the same way we check for eq3 LHS=RHS for both 6 and -6 hence they are the solutions for eq3. Hence the equation that has solutions 6 and -6 is [tex]x^2 - 36 = 0[/tex]