If x1,x2...X20 are in ap then find value of x1^2-x2^2+x3^2....+x19^2-x20^2
Answers
( x₁ - x₂)( x₁ + x₂ + x₃ + x₄ + , .................+ x₁₉ + x₂₀ ) is value of x₁² - x₂² + x₃² - x₄² +...........................................+ x₁₉² - x₂₀² if x₁ , x₂ , x₃ , .......................x₂₀ are in AP
Step-by-step explanation:
x₁ , x₂ , x₃ , .......................x₂₀ are in AP
x₁² - x₂² + x₃² - x₄² +...........................................+ x₁₉² - x₂₀²
using a² - b² = (a + b)(a - b)
= (x₁ + x₂)(x₁ - x₂) + (x₃ + x₄)(x₃ - x₄) +.............................+ (x₁₉ + x₂₀)(x₁₉ - x₂₀)
-d = x₁ - x₂ = x₃ - x₄ = .......................= x₁₉ - x₂₀
= (x₁ + x₂)(-d) + (x₃ + x₄)(-d) +.............................+ (x₁₉ + x₂₀)(-d)
= -d ( x₁ + x₂ + x₃ + x₄ + , .......................+ x₁₉ + x₂₀ )
= ( x₁ - x₂)( x₁ + x₂ + x₃ + x₄ + , .......................+ x₁₉ + x₂₀ )
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Answer:
i think (c)
otherwise search on engine