Question

If x²+kx+16/9 is a perfect square. Find the value of k​

Answer 1

For x² + kx + 16/9 to be a perfect square, k should be equal to 8/3

Explanation:

If x² + kx + 16/9 is a perfect square then it must satisfy the formula of (a + b)² i.e. equal to a² + 2ab + b².

So, first we will form a equal that looks similar to the formula:

`\rm \implies {x}^(2) + kx + (4 * 4)/(3 * 3) \\ \\ \rm \implies {x}^(2) + kx + { \bigg( (4)/(3) } \bigg)^(2)`

Now by comparing we get,

`\rm \implies k \cancel{x} = 2 * \cancel{x}* (4)/(3) \\ \\ \rm \implies k = (8)/(3)`