Step-by-step explanation:xy=-12y=-12/x4x^2-9y^2=1084x^2-9(-12/x)^2=1084x^2-9(144/x^2)=1084x^4-1296=108x^24x^4-108x^2-1296=04z^2-108z-1296=0Notice we have a quadratic equation in the form of az%5E2%2Bbz%2Bc where a=4, b=-108, and c=-1296Let's use the quadratic formula to solve for zz+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 START with the quadratic formulaz+=+%28-%28-108%29+%2B-+sqrt%28+%28-108%29%5E2-4%284%29%28-1296%29+%29%29%2F%282%284%29%29 Plug in a=4, b=-108, and c=-1296z+=+%28108+%2B-+sqrt%28+%28-108%29%5E2-4%284%29%28-1296%29+%29%29%2F%282%284%29%29 Negate -108 to get 108.Z+=+%28108+%2B-+sqrt%28+11664-4%284%29%28-1296%29+%29%29%2F%282%284%29%29 Square -108 to get 11664.z+=+%28108+%2B-+sqrt%28+11664--20736+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-1296%29 to get -20736z+=+%28108+%2B-+sqrt%28+11664%2B20736+%29%29%2F%282%284%29%29 Rewrite sqrt%2811664--20736%29 as sqrt%2811664%2B20736%29z+=+%28108+%2B-+sqrt%28+32400+%29%29%2F%282%284%29%29 Add 11664 to 20736 to get 32400z+=+%28108+%2B-+sqrt%28+32400+%29%29%2F%288%29 Multiply 2 and 4 to get 8.z+=+%28108+%2B-+180%29%2F%288%29 Take the square root of 32400 to get 180.z+=+%28108+%2B+180%29%2F%288%29 or z+=+%28108+-+180%29%2F%288%29 Break up the expression.z+=+%28288%29%2F%288%29 or z+=++%28-72%29%2F%288%29 Combine like terms.z+=+36 or z+=+-9 Simplify.So the answers in terms of z are z+=+36 or z+=+-9Now above, I let z = x^2. So x^2 = 36 and x^2 = -9Solve for x in each equation to get: x = 6, x = -6, x = 3i, or x = -3iSo the four solutions for x are x = 6, x = -6, x = 3i, or x = -3i