Question

Which of the following represents all possible values of M that are solutions to the equation 3M=|M^2-10| 2 and 5 -5,-2,2 and 5 -2 and 5 -5 and 2

Answer 1

Given : 3M=|M^2-10|

To find : Values of M

Solution:

3M = | M² - 10 |

Case 1

M² - 10 ≥ 0

=> M² ≥ 10

=>  M ≤-√10  ,   M ≥ √10

3M = M² - 10

=>  M² -3M - 10 = 0

=> M² - 5M + 2M - 10 = 0

=> M (M - 5) + 2(M - 5) = 0

=> ( M + 2)(M - 5) = 0

=> M = - 2 , M = 5

M = 5 as   5 ≥ √10

M = - 2( not possible )   as

Case 2

M² - 10 < 0

=> M² < 10

=>  -√10 <  M < √10  

3M = -(M² - 10)

=>  M² + 3M - 10 = 0

=> M² + 5M -2M - 10 = 0

=> M (M + 5) - 2(M - 5) = 0

=> ( M = 2)(M - 5) = 0

=> M =  2 , M =  - 5

M = 2 as     -√10 <  2 < √10  

M = 5( not possible )  

2 & 5 are the solution

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