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 ...
=a3+b3+c3−3abc View Solution Prove that:∣∣ ∣∣abca−bb−cc−ab+cc+aa+b∣∣ ∣∣=a3+b3+c3−3abc View Solution Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, ...
2(ab)²+2(bc)²+2(ca)²-2ab²c-2abc²-2a²bc>=0只要证(ab-bc)²+(bc-ca)²+(ab-ca)²>=0显然成立,得证。(b)利用(a)的结论,√(3abc(a+b+c))=√(3abc)<=ab+bc+caa²+b²+c²+√(12abc)<=a²+b²+c²+2(ab+bc+ca)=(a+b+c)²=1...
Let A = 1/2 -1 -sqrt 3 sqrt 3 -1 Show that A3 = I. Prove that sqrt 3 + sqrt 2 is irrational. Prove by a mathematical indication that for all n greater than equal to 2, square root{n} less than Summation_{i=1}^{n} 1/square root{i}. Given. x + (1/x...
a) If a, b, c are real numbers prove that 3(ab + bc + ca) less than or equal to (a + b + c)^2 b) If a, b,c are real numbers prove that (a + b + c)^2 less than or equal to 3(a^2 + b^2 + c^2) Prove that if y = y_0e^{kt} , where...
If a + b + c = 0 Then prove that a5+ b5+ c5a³ + b3+ c3a2+ b2+ c2 ...
Prove that 8a^3-(a+b)^3-(a-c)^3-(c-b)^3=3(a-b)(a+c)(2a+b-c) View Solution Exams IIT JEE NEET UP Board Bihar Board CBSE Free Textbook Solutions KC Sinha Solutions for Maths Cengage Solutions for Maths DC Pandey Solutions for Physics ...
Prove that a^6+8a^3+27-18a^3=(a^2+2a+3)(a^4+4a^2+9-2a^3-6a-3a^2) 03:47 Prove that (x-y)^3+(y-z)^3+(z-x)^3=3(x-y)(y-z)(z-x) 02:00 Prove that (a+b+c)^3-(a^3+b^3+c^3)=3(b+c)(c+a)(a+b) 07:02 Prove that (a-b)^3+(b-c)^3+(c-a)...
Let \, c\, be a real number and \, n\, be a positive integer. Prove: \qquad \lim\limits_{x\ \to\ c}\ x^n = c^n. Let x be any real number. Prove that |x|^{2}=x^{2} a) If a, b, c are real numbers prove that 3(ab + bc + ca) les...
The absolute value of a number indicates that any real number within an absolute value will always be positive regardless of its sign. We can also define it as the distance on the number line from zero to the number, whose value is always positive. We can perform several operations with ...