Question

solve the image plz.....no spams plz​

Answer 1

(5x - 3)³ + (2x + 5)³ + 27(4 - 3x)³ = 9(3 - 5x)(2x + 5)(3x - 4)

(5x - 3)³ + (2x + 5)³ + [3(4 - 3x)]³ = 3 × 3[-(5x - 3)](2x + 5)(3x - 4)

... (taking minus sign common out of 3 - 5x)

(5x - 3)³ + (2x + 5)³ + [3(4 - 3x)]³ = 3(5x - 3)(2x + 5)(- 3)(3x - 4)

... (taking 3 and minus sign to the bracket 3x - 4)

(5x - 3)³ + (2x + 5)³ + (12 - 9x)³ = 3(5x - 3)(2x + 5)(12 - 9x)

this expression is of the form of the formula

a³ + b³ + c³ = 3abc

this is possible only when a + b + c = 0

or a = b = c

here, comparing the expression with the formula, we get

a = 5x - 3

b = 2x + 5

c = 12 - 9x

here we observe that a + b + c = 0

now, since the formula is true

a = b = c

hence,

5x - 3 = 2x + 5 = 12 - 9x

5x - 3 = 2x + 5

5x - 2x = 5 + 3

3x = 8

x = $\frac{8}{3}$ ... (i)

2x + 5 = 12 - 9x

2x + 9x = 12 - 5

11x = 7

x = $\frac{7}{11}$ ... (ii)

5x - 3 = 12 - 9x

5x + 9x = 12 + 3

14x = 15

x = $\frac{15}{14}$ ... (iii)

(since the expression is a cubic expression, hence x has 3 values)

now,

2x + 1 = 19/3 (when x = 8/3)

2x + 1 = 25/11 (when x = 7/11)

2x + 1 = 22/7 = π (when x = 15/14)