Question

plzz solve it...................
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Answer 1

Answer:600

Step-by-step explanation: (343)^3 + (257)^3 / (343)^2 -(343)(257) + (257)^2

= (343+257) (343)^2 - (343)(257) + (257)^2

= (343+257)

= 600

Answer 2

$\mathsf{Question :\;\dfrac{343 \times 343 \times 343 + 247 \times 247 \times 247}{343\times 343 - 343 \times 257 + 257 \times 257}}$

$\mathsf{\implies \dfrac{343^3 + 247^3}{343^2 - 343 \times 257 + 257^2}}$

Consider : (a + b)³ = a³ + 3a²b + 3ab² + b³

$\longrightarrow$  a³ + b³ = (a + b)³ - 3a²b - 3ab²

$\longrightarrow$  a³ + b³ = (a + b)³ - 3ab(a + b)

$\longrightarrow$  a³ + b³ = (a + b)[(a + b)² - 3ab)]

$\longrightarrow$  a³ + b³ = (a + b)[a² + b² + 2ab - 3ab]

$\longrightarrow$  a³ + b³ = (a + b)[a² + b² - ab]

$\mathsf{\implies \dfrac{(343+ 247)(343^2 - 343 \times 257 + 257^2)}{343^2 - 343 \times 257 + 257^2}}$

$\mathsf{\implies (343 + 247)}$

$\mathsf{\implies 600}$