To determine To calculate: The solution of the equations m 2 + 3 n 2 = 10 , m − n = 2. Explanation Given Information: The equations are: m 2 + 3 n 2 = 10 And m − n = 2 Formula Used: Use the formula of quadratic equation to find the factors of standard equation a x 2 + b x + c = 0 x = − b ± b 2 − 4 a c 2 a Calculation: Consider the linear equations, m 2 + 3 n 2 = 10 …… ( 1 ) And m − n = 2 …… ( 2 ) Simplify the above equation in terms of m : m = n + 2 …… ( 3 ) Now substitute the value of m = n + 2 in equation, ( 1 ) , and solve it. m 2 + 3 n 2 = 10 ( n + 2 ) 2 + 3 ( n ) 2 = 10 n 2 + 4 + 4 n + 3 n 2 = 10 4 n 2 + 4 n − 6 = 0 Now, divide by 2 in the above equation on both sides, 2 n 2 + 2 n − 3 = 0 Now use the quadratic formula and compare it with the standard equation a x 2 + b x + c = 0 , n = − ( 2 ) ± ( 2 ) 2 − 4 ( 2 ) ( − 3 ) 2 ( 2 ) = − 2 ± 4 − 4 ( − 6 ) 4 = − 2 ± 4 + 24 4 = − 2 ± 2 7 4 Again simplify, n = − 1 ± 7 2 Further, simplify the factors, n = − 1 + 7 2 And n = − 1 − 7 2 Now substitute n = − 1 + 7 2 in the equation, ( 3 ) , and solve for m : m = n + 2 = ( − 1 + 7 2 ) + 2 = ( − 1 + 7 + 4 2 ) = 3 + 7 2 The ordered pair is ( 3 + 7 2 , − 1 + 7 2 ) . Now substitute n = − 1 − 7 2 in the equation, ( 3 ) , and solve for m : m = n + 2 = ( − 1 − 7 2 ) + 2 = ( − 1 − 7 + 4 2 ) = 3 − 7 2 The ordered pair is ( 3 − 7 2 , − 1 − 7 2 ) . The following graph serves as a check and intersection on this graph occurs at ( 3 + 7 2 , − 1 + 7 2 ) and ( 3 − 7 2 , − 1 − 7 2 )

6th Edition

ISBN: 9780321877949

Author: Johnson

Publisher: YUZU

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Chapter 13.4, Problem 18ES

To determine

To calculate: The solution of the equations m2+3n2=10, m−n=2.

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Chapter 13.4, Problem 17ES

Chapter 13.4, Problem 19ES

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Chapter 13 Solutions

EBK ELEMENTARY AND INTERMEDIATE ALGEBRA

Ch. 13.1 - Prob. 1YT Ch. 13.1 - Prob. 2YT Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 4YT Ch. 13.1 - Prob. 5YT Ch. 13.1 - Prob. 1ES Ch. 13.1 - Prob. 2ES Ch. 13.1 - Choose from the following list the word that best...Ch. 13.1 - Choose from the following list the word that best...Ch. 13.1 - Prob. 5ES

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