how do you solve inequality 52 +8x ≥ 4x +72
Question : Solve inequality 52 +8x ≥ 4x +72 . Solution We solve an inequality is same as an equation til the last step.52 +8x ≥ 4x +72 We shall…
What is power set? give examples
Question : What is power set? give examples Solution: Power set : Let S be a set then power set is the set of all subsets of of S. It…
How to Find 51^4 using binomial theorem
Question : Find 51^4 using binomial theorem SOLUTION: We shall 51^4 using binomial theorem as follows Thus we obtain 51^4 = 6765201.
Prove that 1 + 2 + · · · + n = n(n + 1)/2 for all integers n ≥ 1.
Question: Prove that 1 + 2 + · · · + n = n(n + 1)/2 for all integers n ≥ 1. Proof: We shall prove by induction. Base case:…
Let n be an integer and not divisible by 3 then n^2 = 3k + 1 for some integer k.
Question.: Let n be an integer and not divisible by 3 then n^2 = 3k + 1 for some integer k. Proof: If n is be an integer then n…
Prove that square root of 2 is irrational
Question: Prove that square root of 2 is irrational. Solution: Suppose that √ 2 was rational. By definition of rational numbers √ 2 can be written as a/b for some…
If a b c are in AP then prove that a^2(b+c) b^2(c+a) c^2(a+b) are in AP
Question : If a b c are in AP then prove that a^2(b+c) b^2(c+a) c^2(a+b) are in AP Proof: If a,b,c are in AP \[2b=a+c\] To prove that \[a^2(b+c), b^2(c+a),…
If a b c are in AP then prove that a(1/b+1/c) b(1/c+1/a) c(1/a+1/b) are in AP
Question : If a b c are in AP then prove that a(1/b+1/c) b(1/c+1/a) c(1/a+1/b) are in AP Proof: Given a,b,c are in AP \[2b=a+c \] to prove that \[a(1/b+1/c),…
If a b c are in AP then prove that 1/bc 1/ca 1/ab are in AP
Q: If a b c are in AP then prove that 1/bc 1/ca 1/ab are in AP Proof: a,b,c are in AP \[2b=a+c \] Dividing this by abc both sides…
If a,b,c are in Arithmetic progression then prove that b+c, c+a, a+b are in Arithmetic progression
Question : If a,b,c are in Arithmetic progression then prove that b+c, c+a, a+b are in Arithmetic progression Solution : b+c, c+a, a+b are in Arithmetic progression proof: a,b,c are…