Question

Rozwiąz układ równań;
8*a +4*h=48
2*a^2+4*a*h=90

Answer 1

8a + 4h = 48
2a² + 4ah = 90

8a = 48 - 4h
2a² + 4ah = 90

a = 8 - 1/2h
2a² + 4ah = 90

2(8 - 1/2h)² + 4h(8 - 1/2h) = 90

2( 64 - 8h + 1/4h²) + 32h - 2h² = 90

128 - 16h + 1/2h² + 32h - 2h² = 90

- 3/2h² +16h + 38 = 0

Δ = 256 - 4 * 3/2 * 38 = 256 + 228 = 484

√Δ = 22

x1 = - 16 - 22 / -3 = 38/3

h = 38/3

lub

x2 = -16 + 22 / -3 = 6 / -3 = -2

h = -2

8a + 4h = 48

8a + 4 * 33/3 = 48
8a = 4
a = 1/2

lub

8a + 4h = 48
8a - 8 = 48
8a = 40
a = 5