Question

If 2a^2+9b^2+4c^2-4a-6b+4ac=-5,then the value of a^2-b^2+c^2 is equal to

Answer 1

Given: The term 2a^2 + 9b^2 + 4c^2 - 4a - 6b + 4ac = -5

To find: The value of a^2 - b^2 + c^2

Solution:

• Now we have given the value of 2a^2 + 9b^2 + 4c^2 - 4a - 6b + 4ac as -5.

• So, we can rewrite it as:

               (a^2 + a^2 + 9b^2 - 6b + 4c^2 - 4a  + 4ac ) = -5

• Now splitting the terms, we get:

               (a^2 - 4a) + (9b^2 - 6b) +(a^2 + 4c^2 + 4ac ) = -5

• To make whole square, we will do:

               (a^2 - 4a + 4 - 4) + (9b^2 - 6b + 1 - 1) + (a + 2c)^2 = -5

               (a + 2)^2 + (3b - 1)^2 +  (a + 2c)^2 - 4 - 1 = -5

               (a + 2)^2 + (3b - 1)^2 +  (a + 2c)^2 = 0

• Now:

               (a + 2)^2 = 0

               a = 2

               (3b - 1)^2 = 0

               b = 1/3

               (a + 2c)^2 = 0

               c = -a/2 = -2/2 = -1

• Now putting these values in a^2 - b^2 + c^2, we get:

               a^2 - b^2 + c^2 = (2)^2 - (1/3)^2 + (-1)^2

                                          = 4 - 1/9 + 1

                                         = 44/9

Answer:

               So the value of a^2 - b^2 + c^2 is 44/9.                          

Answer 2

Answer:

$\frac{44}{9}$

Step-by-step explanation:

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