Maths question about ratio

[匿名]

2013-05-06 5:59 am

The two expressions1/6πh[a2+b2+(a + b)2]and 1/3π[b2(h + x) – a2x]are found by different methods for thevolume of a certain solid. Prove that if the two expressions are equivalent,then a : x = b : (h + x)

回答 (1)

不用客氣

2013-05-06 7:18 am

✔ 最佳答案

(1/6)πh[a² + b² + (a + b)²] = (1/3)π[b²(h + x) - a²x]

6 * (1/6)πh[a² + b² + (a + b)²] = 6 * (1/3)π[b²(h + x) - a²x]

πh[a² + b² + (a + b)²] = 2π[b²(h + x) - a²x]

h[a² + b² + (a² + 2ab + b²)] = 2[(hb² + b²x) - a²x]

h(2a² + 2ab + 2b²) = 2(hb² + b²x - a²x)

2(ha² + hab + hb²) = 2(hb² + b²x - a²x)

ha² + hab + hb² = hb² + b²x - a²x

ha² + hab = b²x - a²x

ha(a + b) = x(b² - a²)

ha(b + a) = x(b + a)(b - a)

ha = x(b - a)

ha = bx - ax

ha + ax = bx

a(h + x) = bx

a/x = b/(h + x)

a : x = b : (h + x)

參考: 不用客氣

👍 0 👎 0