![SOLVED:(III) Show that for an isotropic solid, β=3 α, if the amount of expansion is small. βand αare the coefficients of volume and linear expansion, respectively. [ Hint: Consider a cubical solid, SOLVED:(III) Show that for an isotropic solid, β=3 α, if the amount of expansion is small. βand αare the coefficients of volume and linear expansion, respectively. [ Hint: Consider a cubical solid,](https://cdn.numerade.com/previews/cd4dbf62-b399-4719-9ffa-4eeff83515bb_large.jpg)
SOLVED:(III) Show that for an isotropic solid, β=3 α, if the amount of expansion is small. βand αare the coefficients of volume and linear expansion, respectively. [ Hint: Consider a cubical solid,
![ΤΑΥΤΟΤΗΤΕΣ α 3 +β 3 =(α+β)(α 2 -αβ+β 2 ) α 3 +β 3 =(α+β) 3-3αβ(α+β) α 3 -β 3 =(α-β)(α 2 +αβ+β 2 ) (α+β+γ) 2 =α 2 +β 2 +γ ΤΑΥΤΟΤΗΤΕΣ α 3 +β 3 =(α+β)(α 2 -αβ+β 2 ) α 3 +β 3 =(α+β) 3-3αβ(α+β) α 3 -β 3 =(α-β)(α 2 +αβ+β 2 ) (α+β+γ) 2 =α 2 +β 2 +γ](https://docplayer.gr/docs-images/42/51613/images/page_1.jpg)
ΤΑΥΤΟΤΗΤΕΣ α 3 +β 3 =(α+β)(α 2 -αβ+β 2 ) α 3 +β 3 =(α+β) 3-3αβ(α+β) α 3 -β 3 =(α-β)(α 2 +αβ+β 2 ) (α+β+γ) 2 =α 2 +β 2 +γ
![Write the formula: alpha^3+beta^3=…………….a)(alpha+beta)^3-3alphabeta(alpha+ beta) b)(alpha-beta)^3+3alphabeta(alpha-beta) c)(alpha+beta)^3-3alphabeta( alpha-beta) d)(alpha-beta)^3-3alphabeta(alpha-beta) Write the formula: alpha^3+beta^3=…………….a)(alpha+beta)^3-3alphabeta(alpha+ beta) b)(alpha-beta)^3+3alphabeta(alpha-beta) c)(alpha+beta)^3-3alphabeta( alpha-beta) d)(alpha-beta)^3-3alphabeta(alpha-beta)](https://d10lpgp6xz60nq.cloudfront.net/web-thumb/642936059_web.png)
Write the formula: alpha^3+beta^3=…………….a)(alpha+beta)^3-3alphabeta(alpha+ beta) b)(alpha-beta)^3+3alphabeta(alpha-beta) c)(alpha+beta)^3-3alphabeta( alpha-beta) d)(alpha-beta)^3-3alphabeta(alpha-beta)
![lf alpha,beta,gamma are the roots of x^3 + 2x - 3 = 0 , then the transformed equation having the roots alpha/beta + beta/alpha,beta/gamma + gamma/beta,gamma/alpha + alpha/gamma is obtained by taking lf alpha,beta,gamma are the roots of x^3 + 2x - 3 = 0 , then the transformed equation having the roots alpha/beta + beta/alpha,beta/gamma + gamma/beta,gamma/alpha + alpha/gamma is obtained by taking](https://dwes9vv9u0550.cloudfront.net/images/5603869/6cfb9c17-da9c-4acf-8e69-29c49f9184b3.jpg)