MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Property 1

If α 2+β 2+...

Question

If $α^{2} + β^{2} + γ^{2} = 1$ , then highest integral value of $α β + β γ + α γ$ is

Open in App

Solution

$\begin{matrix} α^{2} + β^{2} + γ^{2} = 1 {(α - β)}^{2} {(β - γ)}^{2} + {(γ - α)}^{2} \geq 0 2 [α^{2} + β^{2} - α β - β γ - γ α] \geq 0 1 - (α β + β γ + γ α) \geq 0 α β + β γ + γ α - 1 \leq 0 α β + β γ + γ α 1 ∴ H e i g h t i n t e g r a l v a l u e i s 1 \end{matrix}$

Suggest Corrections

thumbs-up

0

Similar questions

α, β, γ

are the roots of the equation

x^{3} + q x + r = 0

, then the equation whose roots are

β γ - α^{2}, γ α - β^{2}, α β - γ^{2}

{sin}^{- 1} α + {sin}^{- 1} β + {sin}^{- 1} γ = \frac{3 π}{2}

α β + α γ + β γ

7 α = α^{2} + 3

β^{2} = 7 β - 3,

then the value of

α β

α, β, γ

be the zeroes of the expression

a x^{3} + b x^{2} + 4 x + 7

, find the value of

α β + β γ + α γ

α, β, γ

are the roots of equation

x^{3} - 6 x^{2} + 11 x - 6 = 0

, then find the equation whose roots are

α^{2} + β^{2}, β^{2} + γ^{2}, γ^{2} + α^{2}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Property 1

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon