Answer:
see explanation
Step-by-step explanation:
given 32 - 162k² = 0 ( factor out 2 from each term )
2(16 - 81k²) = 0
16 - 81k² ← is a difference of squares and factors in general as
• a² - b² = (a - b)(a + b)
16 = 4² ⇒ a = 4
81k² =(9k)² ⇒ b = 9k
16 - 81k² = (4 - 9k)(4 + 9k), thus
32 - 162k² = 0
2(4 - 9k)(4 + 9k) = 0
Equate each factor to zero and solve for k
4 - 9k = 0 ⇒ k = [tex]\frac{4}{9}[/tex]
4 + 9k = 0 ⇒ k = - [tex]\frac{4}{9}[/tex]
As a check
Substitute these values into the original equation and if left side equals right side then these are the solutions.
32 - 162 × ( - [tex]\frac{4}{9}[/tex])² = 32 - 162 × [tex]\frac{16}{81}[/tex] = 32 - 32 = 0
32 - 162 × ([tex]\frac{4}{9}[/tex])² = 32 - 32 = 0
Hence solutions are k = ± [tex]\frac{4}{9}[/tex]
