Find answers to your questions and expand your knowledge with IDNLearn.com. Discover in-depth and trustworthy answers to all your questions from our experienced community members.

for a diamond problem what two numbers' sums equal 31 and their product is 234?

Sagot :

[tex]a+b=31=> \boxed{a=b-31} \\ab=234 \\\\ \\\\ b*(b-31)=234 \\\\ b^2-31b-234=0 \\ a=1 \\ b=-31 \\ c=-234 \\\\ \Delta= (-31)^2-4*1*(-234)= 961-936=25 \\\\ x_1;x_2=\frac{-(-31)+/-\sqrt{25}}{2*1} =\frac{31+/-5}{2} \\\\ x_1=\frac{31+5}{2}=\frac{36}{2}\to\boxed{18} \\\\ x_2=\frac{31-5}{2}=\frac{26}{2}\to\boxed{13} \\\\ (x-18)(x-13)=0 \\\\ 1)x-18=0 \ => \boxed{x=18} \\\\ 2)x-13=0 \ => \boxed{x=13} [/tex]

Let

x-------> the first number

y------> the second number


we know that

[tex] x+y=31 [/tex]

[tex] x=31-y [/tex]

equation [tex] 1 [/tex]


[tex] x*y=234 [/tex]

equation [tex] 2 [/tex]


substitute equation 1 in equation 2

[tex] (31-y)*y=234\\ 31y-y^{2} =234\\ -y^{2} +31y-234=0 [/tex]



using a graph tool-----> to resolve the second order equation

see the attached figure


the solution is

[tex] 13 and 18 [/tex]

View image Calculista
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! IDNLearn.com is committed to your satisfaction. Thank you for visiting, and see you next time for more helpful answers.