method of cross multiplication method pair of linear equations

Find the factors of 24 with their sum = +14. The factors are 12 and 2. +14x will be written as +12x + 2x. 3x 2 + 14x + 8 = 3x 2 + 12x + 2x + 8 = 3x (x + 4) + 2 (x + 4) = (3x + 2) (x + 4) All the steps have occurred in the reverse order to the multiplication given above. Resolve into facto..

The quadratic expression ax 2 + bx + c can be expressed in the form a(x 2 A 2 ) by the method of completing the square. The integrals can be evaluated by using the special integral..

Step 3: The second integral can be evaluated by method of completing squares...

which can be integrated by method of completing square..

Impure titanium is heated to 250 o C with iodine. When titanium reacts to form volatile titanium tetraiodide Impurities present in titanium do not react with iodine. Therefore, the vapors titanium tetraiodide formed is ultra pure. Vapors of titanium tetraiodide are passed through a bulb cont..

(ii) Find the values of the constants L and M by comparing the co-efficients of like powers of x on both sides. (iv) The integrals in the form are easily integrabl..

Taking 1 as the second function and integrating by parts, we get ..

P(n,r) is the number of permutations of n dissimilar things taken r at a time. These permutations can be divided into two groups. (i) Those not containing a particular thing l . (ii) Those containing a particular thing l . Taking out l from the given things, we have (n-1) things which can be..

Given sin q = k .......(i) Let a be any angle, such that sin a = k. (In actual practice, we choose the smallest positive angle such that sin a = k.) From (i) and (ii), we have..