ZJSG09112007
Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Given x² = 17x +y and y²= x+17y . Find :
[tex] \sqrt{ {x}^{2} + {y}^{2} + 1 } [/tex]
​

Sagot :

Answer:

Step-by-step explanation:

x² = 17x + y

y² = x + 17y

x² +  y² =  17x + y + x + 17y

x² +  y² =  18x +  18y

x² +  y² + 1 =  9* 2(x + y) + 1

√(x² +  y² + 1) = 3√(2x + 2y + 1)

discipulus

Answer:

[tex] {x}^{2} = 17x + y....(1) \\ {y}^{2} = x + 17y....(2) \\ (1) - (2) \\ {x}^{2} - {y}^{2} = 16x - 16y \\ {x}^{2} - {y}^{2} = 16(x - y) \\ (x - y)(x + y) = 16(x - y) \\ (x - y) \neq0 \\ x + y = 16 ....(3)\: since \: x \neq \: y \\ (1) + (2) \\ {x}^{2} + {y}^{2} = 18x + 18y \\ {x}^{2} + {y}^{2} = 18(x + y) \\ subtitute \: (3) \\ {x}^{2} + {y}^{2} = 18 \times 16 \\ {x}^{2} + {y}^{2} = (17 + 1)(17 - 1) = 289 - 1 \\ {x}^{2} + {y}^{2} + 1 = 289) \: take \: sqr \\ \sqrt{ {x}^{2} + {y}^{2} + 1} = \sqrt{289} \\ \therefore \sqrt{ {x}^{2} + {y}^{2} + 1} = 17[/tex]

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.