find two positive numbers

Working rules for expanding (a + b) n n N: Step 1: The value of index, n implies that there will be n+1 terms in the expansion of (a + b) n . Step 2: Write the first term: n C 0 a n b 0 . Step 3: For the second term, take coefficient as n C 1 , decrea..

n C 0 , n C 1 , ..... n C n are called binomial coefficients. n C 0 , n C 2 n C 4 , ..... are called even binomial coefficients. n C 1 , n C 3 , n C 5 .... are called odd binomial coefficients. In case of no ambiguity, the binomial coefficients n C 0 , n C 1 , .....

Hence h 1 , h 2 ,....h n are the n harmonic means. If A, G and H respectively are arithmetic, geometric and harmonic means of two positive quantities a and b, then G 2 = A.H and A ≥ G ≥..

The general form of the trinomial is (x 2 + cx + d) where c and d have different numerical values: c = a + b, and d = ab. In the given trinomial expression if all terms are positive, then both the factors are positive. If the middle term is negative,..

i) A sequence of multiples of 5 5, 10, 15, 20, ii) A sequence of reciprocals of positive integers The above two sequences are clearly the infinite sequence..

Matrices - Consider the arrangement In this arrangement, there are two rows and four columns. The number 3 lies in the 2 n d row and 4 t h column. Each number has a fixed position. Matrix A has 2 rows and 3 columns and is thus of order ..

is called the modulus of the complex number z denoted by |z| and q = tan -1 y/x is called the amplitude or argument of the complex number z denoted by amp(z) or arg(z). The value of q is such that - p < q p , is called the principal value of the amplitude. The general value o..

Alternative Proof of Binomial Theorem for Positive Integral Index (Combinatorial Method) - Alternative Proof of Binomial Theorem for Positive Integral Index (Combinatorial Method). We have, (a + b) n = (a + b) (a + b) ....... n times. The terms on the RHS are obtained by taking ..

An algebraic expression of the form a 0 +a 1 x+a 2 x 2 +.+a n x n where a 0 , a 1 , a 2 ,.a n are real numbers, n is a positive integer is called a polynomial in ..

We know that 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2 6 We know that 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2 6 Here 2 is called the base and 6 is called the power (or i..