Question

Lets find, for which value or values of K will the expression C²+kc+1/9 be a perfect square.

Answer 1

a=c and b=1/3 thus equating 2ab to kc

u will get k=2/3

Answer 2

ANSWER:-

$(a+b)² = c²+kc+ \frac{1}{9} \\ →(a+b)² = c²+kc+ { ( \frac{1}{3}) }^{2} \\ →(a+b)² = c²+2 \times k \times c+ { ( \frac{1}{3}) }^{2} \\ →(a+b)² = c²+2 k c+ { ( \frac{1}{3}) }^{2} \\ \\ comparing, \\ k{ \cancel{c }}= 2 \times{ \cancel{ c}} \times \frac{1}{3} \\ →k = \frac{2}{3}$

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