Consider a decreasing GP:g1,g2,g3.....gn. Such that g1+g2+g3=13 and g1^2+g2^2+g3^2=91. Determine g1,g2 and g3.
Answers
Answer:
g₁ , g₂ & g₃ are 9 , 3 & 1
Step-by-step explanation:
Consider a decreasing GP:g1,g2,g3.....gn. Such that g1+g2+g3=13 and g1^2+g2^2+g3^2=91. Determine g1,g2 and g3.
g₁ , g₂ & g₃ are in gp
=> g₂² = g₁g₃
g₁ + g₂ + g₃ = 13
=> g₁ + g₃ = 13 - g₂
Squaring both sides
=> g₁² + g₃² + 2g₁g₃ = 169 + g₂² - 26g₂
=> g₁² + g₃² + 2 g₂² = 169 + g₂² - 26g₂
=> g₁² + g₃² + g₂² = 169 - 26g₂
=> 91 = 169 - 26g₂
=> 26g₂ = 78
=> g₂ = 3
g₁ + g₂ + g₃ = 13
=> g₁ + g₃ = 10
g₁g₃ = 3² = 9
g² - 10g + 9 = 0
where g₁ & g₃ are roots
g² - g - 9g + 9 = 0
=> g(g-1) -9(g-1) = 0
=> (g-1)(g-9) = 0
=> g = 1 & 9
g₁ = 9 & g₃ =1 ( as decreasing GP)
g₁ , g₂ & g₃ are 9 , 3 & 1
Answer:
Consider a decreasing GP:g1,g2,g3.....gn. Such that g1+g2+g3=13 and g1^2+g2^2+g3^2=91. Determine g1,g2 and g3.Also the Charter Act of 1813 did not clarify the objectives of education and the methods for improvement of literature of the learned natives in India. The Charter Act had given stress on allotting the one lakhs rupees only; no specific regulations were granted for establishing the schools and colleges in India.