Soham
Answered

Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Find the value of:
[tex] 27x^{3}+8 y^{3} [/tex] if 3x+2y = 20 and xy = [tex] \frac{14}{9} [/tex]

Sagot :

[tex]27x^3+8y^3=(3x)^3+(2y)^3=(3x+2y)[(3x)^2-3x\cdot2y+(2y)^2]\\\\=(3x+2y)[(3x)^2+2\cdot3x\cdot2y+(2y)^2-3\cdot3x\cdot2y]\\\\=(3x+2y)[(3x+2y)^2-18xy]=(*)\\---------------------------\\3x+2y=20\\\\xy=\frac{14}{9}\\------------------------------\\(*)=20\cdot(20^2-19\cdot\frac{14}{9})=20\cdot(400-18\cdot\frac{14}{9})=20\cdot(400-2\cdot14)\\\\=20\cdot(400-28)=20\cdot372=7440[/tex]



[tex]a^3+b^3=(a+b)(a^2-ab+b^2)\\\\(a+b)^2=a^2+2ab+b^2[/tex]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.