Question

E²-F²=11
E-F=1
E=?
F=?

G²-H²=24
G-H=2
G=?
H=?

L:M=5
L²+M²=104
L=?
M=?

Answer 1

${e}^{2} - {f}^{2} = 11 \\ \\ (e - f)(e + f) = 11 \\ \\ e - f = 1 \\ \\ 1 \times (e + f) = 11 \\ \\ e + f = 11 \\ \\ e = 1 + f \\ \\ 1 + f + f = 11 \\ \\ 2f = 10 \\ \\ f = 5 \\ \\ e - 5 = 11 \\ \\ e = 6$

${g}^{2} - {h}^{2} = 24 \\ \\ (g - h)(g + h) = 24 \\ \\ g - h = 2 \\ \\ 2 \times (g + h) = 24 \\ \\ g + h = 12 \\ \\ g = 2 + h \\ \\ 2 + h + h = 12 \\ \\ 2h = 10 \\ \\ h = 5 \\ \\ g + 5 = 12 \\ \\ g = 7$

$\frac{l}{m} = 5 \\ \\ 5m = l \\ \\ {l}^{2} + {m}^{2} = 104 \\ \\ 25 {m}^{2} + {m}^{2} = 104 \\ \\ 26 {m}^{2} = 104 \\ \\ {m}^{2} = 4 \\ \\ m = 2 \\ \\ m = - 2 \\ \\ 5 \times 2 = l \\ l = 10 \\ \\ 5 \times ( - 2) = l \\ l = - 10$