Question

If ‘x’ is a counting number
(a) What number should be added to x2 + 6x to become a
perfect square?
(b)If x2 + ax +16 is a perfect square what will be the value of a.
Varghese P M , Holy Ghost B H S Muttuchira

Answer 1

SOLUTION

TO DETERMINE

If ‘x’ is a counting number

(a) The number should be added to x² + 6x to become a perfect square

(b) The value of a if x² + ax +16 is a perfect square

EVALUATION

(a)

$\sf{ {x}^{2} + 6x }$

$\sf{ = {x}^{2} + 2.x.3 + {(3)}^{2} - {(3)}^{2} }$

$\sf{ = {(x + 3)}^{2} - 9}$

The number should be added = 9

(b)

$\sf{ {x}^{2} + ax + 16}$

$\sf{ = {x}^{2} \pm 2.x.4 + {(4)}^{2} \mp \: 2.x.4 + ax }$

$\sf{ = {(x \pm 4)}^{2} + x(a \mp 8)}$

Hence the required value

$\sf{a = \pm 8}$

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