Prove that :(a+b)3+(b+c)3+(c+a)3−3(a+b)(b+c)(c+a)=2(a3+b3+c3−3abc) View Solution Prove that :a3+b3+c3−3abc=12(a+b+c){(a−b)2+(b−c)2+(c−a)2} View Solution Ifa,b,care in A.P., prove that8b3−a3−c3=3ac(a+c) ...
59.Let a: b c 0. Prove that a^(b+c)+b^(a+c)+c^(a+b)≥1 相关知识点: 试题来源: 解析 if a≥1 or b≥1 or c≥1 then the inequality is trueif 0≤a,b,c≤1 then suppose c=mina,b,c+ if a+b1 We have b+c1,c+a1Apply Ber noullWe 'inequality(1/n)^(...
let LHS =(a+b)^3+(b+c)^3+(c+a)^3-3(a+b)(b+c)(c+a) we know, [x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)] so, =((a+b)+(b+c)+(c+a))((a+b)^2+(b+c)^2+(c+a)^2-(a+b)(b+c)+(b+c)(c+a)+(c+a)(a+b)) =2(a+b+c)(a^2+...
17. (Prove that):a2 a2-(b-c)2 bc b2 b2-(c-a)2 ca(a-b)(b-c)(c-a)(a+b+c)(a2+b2+c2c2 c2-(a-b)2 ab Hint : C2→ (C2- C1) C_2→C_2-C_1-2C_3 ] 相关知识点: 试题来源: 解析 (a^2+b^2+c^2)(a-b)(b-c) (c-as(atbtl) ...
2.To subject to a procedure that ascertains effectiveness, value, proper function, or other quality: assay,check,essay,examine,test,try,try out. Idioms:bring to the test, make trial of, put to the proof. 3.Archaic.To participate in or partake of personally: ...
Answer to: Prove that where A, B, and C are sets, (B - A) union (C - A) = (B union C) - A By signing up, you'll get thousands of step-by-step...
Prove that a+b+c≤(bc)/(b+c)+(ca)/(c+a)+(ab)/(a+b)+1/2((bc)/a+(ca)/b+(ab)/c) 相关知识点: 试题来源: 解析 Solution.Settingand, whereare some positive real numbers. The inequality becomesBy the Cauchy-Schwarz inequality, we haveand hence, it suffices to prove thatwhich...
The distributive property: (A intersect B) / C = A/C intersect B/C Upvote • 0 Downvote Add comment Still looking for help? Get the right answer, fast. Ask a question for free Get a free answer to a quick problem. Most questions answered within 4 hours. OR Find an Online ...
百度试题 结果1 题目Given that a≡ d (mo d n) an d b≡ c (mo d n), prove that(a+ b)≡(c+ d) (mo d n). 相关知识点: 试题来源: 解析 Proof 反馈 收藏
To prove the identity a3+b3+c3−3abc=(a+b+c)(a+bω+cω2)(a+bω2+cω), where ω is a cube root of unity, we will start by expanding the right-hand side (RHS) and show that it simplifies to the left-hand side (LHS). Step 1: Understand the properties of ωRecall that ...