How can I solve xy and x+y = 1890 without using trial and error or a calculator?

Question

x+y=1890 and xy=1890...solving for x and y...sorry

Answer 1

Like say x + y =1890 => x = 1890 - y

sub in other eq

(1890 - y)(y) = 1890

expanding out gives
1890y-y^2 - 1890 = 0 => y^2 - 1890y + 1890 = 0

use quadratic formula: ax^2 + bx + c => (-b +/- sqrt(b^2 - 4ac))/2a
will give you the answers.

Answer 2

ok you want an exact numerical technique to compute X=?17 . No, it doesn't favor to be accomplished through approximation. there are probably a tremendous number of thoughts, that is the first one which springs to options: A summation through the Generalized Binomial Theorem X = ?17 = 17^½ = (a million+16)^½ = 4 * [ (a million/16 + a million) ^½ ] So X/4 (call it X*) = (a million/16 + a million) ^½ Then through the Generalized Binomial Theorem (a million/16 + a million) ^½ is the case x=a million/16, y=a million, r=½ which does converge considering |x/y| = a million/16 < a million = ? ok=0..? [ r_C_k * x^ok * y^(r-ok) ] Noting y^(r-ok) will continuously be a million... = ? ok=0..? [ r_C_k * (a million/16)^ok ] = ? ok=0..? [ r_C_k * 2^(-4k) ] the position the r_C_k are defined for non-integers ok , and also you'll discover the definition on the Wikipedia link below. enable's compute ½_C_k for ok=0,a million,2,3,4... ½_C_0 = a million ½_C_1 = ½ ½_C_2 = ½(½-a million)/2! = -a million/8 ½_C_3 = ½(½-a million)(½-2)/3! = +a million/16 ½_C_4 = ½(½-a million)(½-2)(½-3)/4! = -5/128 ... i imagine you could crunch out a generic effect for ½_C_k with somewhat attempt So the first few words: (a million/16 + a million) ^½ = ? ok=0..? [ ½_C_k * 2^(-4k) ] = ? ok=0..? [ ½_C_k * 2^(-4k) ] = ? ok=0..? [ ½_C_k * 2^(-4k) ] = ½_C_0 * a million + ½_C_1 * a million/16 + ½_C_2 * a million/256 + ½_C_3 * a million/4096 + ½_C_4 * a million/65536... = (a million * a million) + (½ * a million/16) - (a million/8 * a million/256) + (a million/16 * a million/4096) - (5/128 * a million/65536) ... = a million + a million/32 - a million/2048 + a million/65536 - 5/8388608... and finally do not ignore we needed 4 * the above volume X = ?17 ? 4 + a million/8 - a million/512 + a million/16384 - 5/2097152... = 4 + 0.120 5 - 0.001953125 + 0.000061035 ... = 4.1231055 after purely 5 words i.e. we already have 7 important figures of ?17!! yet again the point is that that is an *proper* technique. (As to the speed of convergence, because the signal is alternating and the ratio between successive words ?2^(-4) , then the speed of convergence for each 2 words is ?2^(-8) = a million/256, so that you get ~2 decimal factors for each 2 words). (playstation you'll discover it will be proper in decimal or binary or any base, notwithstanding it really is even easier at the same time as evaluated in binary; the coefficients ought to have extremely elementary binary representations.)

Answer 3

You did not type all of the first equation but I assume it is xy= some constant. Take the second equation, and solve for y. You get: y = 1890 - x. Then take the first equation and substitute "1890-x" for "y" then solve the equation for x. Finally substitute the value for x into y = 1890 - x and you will get the value for y.

Answer 4

First of all . are u equationg both xy and x+y to 1890???

Answer 5

Are you trying to do something specific with xy?

Maximize it, minimize it?.. or what

Answer 6

You can't use the quadratic formula if you don't know if it's a triangle or not. You can only use the formula for triangles.

Answer 7

You dont have enough information to supply...