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…
function f(x)=x^3 is a one one and onto or not ?
Question : function f(x)=x^3 is a one one and onto or not ? Solution :
absolute value function is one one and onto or not?
Question: absolute value function is one one and onto or not? Solution :
solved find eigen values of the matrix A=[3 0 0;0 02;0 2 0]
Question : Find eigen values of the matrix A=[3 0 0;0 02;0 2 0] Solution : Given 3 by 3 matrix \[A=\left(\begin{matrix}3&0&0\\0&0&2\\0&2&0\\\end{matrix}\right)\] It’s Eigen values are given by equation \[\left|\begin{matrix}3-\lambda&0&0\\0&-\lambda&2\\0&2&-\lambda\\\end{matrix}\right|=0\]…
Find Orthogonal trajectories to the family of straight lines y=k(x-1) where k in R
Question: Find Orthogonal trajectories to the family of straight lines y=k(x-1) where k in R Solution : Given family of straight lines \[y=k(x-1) \] (1) To obtain Orthogonal trajectories Step…
solved If B is a matrix such that B^2 =B and A=I-B then which of the following is correct?
Question : If B is a matrix such that B^2 =B and A=I-B then which of the following is correct? A^2=A A^2=I AB=0 BA=0 Solution : From the Given matrix…
which ode does y=sin(log(x)) satisfy?
Question : Which ode does y=sin(log(x)) satisfy? Solution : Given function \[y=sin\left(log\left(x\right)\right)\] differentiating with respect to x \[\frac{dy}{dx}=\cos{\left(\log{\left(x\right)}\right)}\frac{1}{x}\] \[x\ \frac{dy}{dx}=\cos{\left(\log{\left(x\right)}\right)}\] Again differentiating with respect to x \[\frac{dy}{dx}+x\frac{d^2y}{dx^2}=-sin\left(log\left(x\right)\right)\frac{1}{x}=\frac{y}{x}\] \[x^2\frac{d^2y}{dx^2}+x\frac{dy}{dx}+y=0\] is the…