Question

If 5a2+b2+ c2- 6a-8c 4ab -25, then the value of (b- c2+a) is ​

Answer 1

SOLUTION

GIVEN

$\sf{5 {a}^{2} + {b}^{2 } + {c}^{2} - 6a - 8c = 4ab - 25 }$

TO DETERMINE

The value of

$\sf{b - {c}^{2} + a}$

EVALUATION

Here the given expression is

$\sf{5 {a}^{2} + {b}^{2 } + {c}^{2} - 6a - 8c = 4ab - 25 }$

Now we simplify it as below

$\sf{5 {a}^{2} + {b}^{2 } + {c}^{2} - 6a - 8c = 4ab - 25 }$

$\sf{ \implies \: 5 {a}^{2} + {b}^{2 } + {c}^{2} - 6a - 8c - 4ab + 25 = 0 }$

$\sf{ \implies \: 4 {a}^{2} - 4ab + {b}^{2 } + {c}^{2} - 8c + 16 + {a}^{2} - 6a + 9 = 0 }$

$\sf{ \implies \: {(2a - b)}^{2} + {(c - 4)}^{2} + {(a - 3)}^{2} = 0 }$

Which gives

2a - b = 0 , c - 4 = 0 , a - 3 = 0

Thus we get

a = 3 , b = 6 , c = 4

Hence

$\sf{b - {c}^{2} + a}$

$\sf{ = 6 - {(4)}^{2} + 3}$

$\sf{ = 6 - 16 + 3}$

$= - 7$

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