Question

If a, b, c are in continued proportion , prove that a/c = 2 a^2−5ab+7 b^2 /2b ^2−5bc+ 7 c^2

Answer 1

given a , b , c are in continued proportion

⇒ a : b : : b : c ⇒ a x c = b x b

ac=b² .............(1)

now A/Q a(b-c)=2b ⇒ ab - ac -2b = 0

⇒ ab - b² -2b = 0

⇒ b(a - b -2) = 0

⇒ a - b -2 =0 as b≠0

⇒ a - b = 2 ............(2)

now to prove a-c=2(a+b)/a

LHS = a-c ⇒ multipying a to nr. and dr.

⇒ a(a-c)/a ⇒ a² - ac/ a ⇒ a² - b² / a

⇒ (a-b)(a+b)/a ⇒ 2(a+b)/a from (1) and (2)

this process only

hence proved

hope this helps mark as brainlist and thanks to answer

Answer 2

Answer:

Step-by-step explanation: