Verified answer

[tex] {x}^{2} - 9 = {y}^{3} + 42[/tex]

[tex] {x}^{2} - 9 = {12}^{3} + 42 \\ {x}^{2} - 9 = 1728 + 42 \\ {x}^{2} - 9 = 1770 \\ {x}^{2} = 1770 + 9 \\ {x}^{2} = 1779 \\ x = ± \sqrt{1779} [/tex]

[tex] {x}^{2} - 9 = {4}^{3} + 42 \\ {x}^{2} - 9 = 64 + 42 \\ {x}^{2} - 9 = 106 \\ {x}^{2} = 106 + 9 \\ {x}^{2} = 115 \\ {x}^{} = ± \sqrt{115} [/tex]

[tex] {x}^{2} - 9 = {9}^{3} + 42 \\ {x}^{2} - 9 = 729 + 42 \\ {x}^{2} - 9 = 771 \\ {x}^{2} = 771 + 9 \\ {x}^{2} = 780 \\ x = ± \sqrt{780} [/tex]

[tex] {x}^{2} - 9 = {4.6}^{3} + 42 \\ {x}^{2} - 9 = 97,336 + 42 \\ {x}^{2} - 9 = 139.336 \\ {x}^{2} = 139.336 + 9 \\ {x}^{2} = 148.336 \\ x = ± \sqrt{148.336} [/tex]

[tex] {x}^{2} - 9 = {32}^{3} + 42 \\ {x}^{2} - 9 = 32 768 + 42 \\ {x}^{2} - 9 = 32810 \\ {x}^{2} = 32810 + 9 \\ {x}^{2} = 32819 \\ x = ± \sqrt{32819} [/tex]