Question

x³ + 3
/2
² + 3
4
+
1
/8​

Answer 1

Step-by-step explanation:

( x³ + 4 xy² ) / ( 4 x²y + y³ ) = 15/16

⇒ 16 ( x³ + 4 xy² ) = 15 ( 4 x²y + y³ )

⇒ 16 x³ + 64 xy² - 60 x²y - 15 y³

⇒ 8 x³ + 54 xy² - 36 x²y - 27 y³ + 12 y³ + 10 xy² - 24 x²y + 8 x³ = 0

⇒ (2x)³ + 3(2x)(3y)² - 3(2x)²(3y) - (3y)³ + 12 y³ + 10 xy² - 24 x²y + 8 x³ = 0

⇒ ( 2 x - 3 y )³ + 12 y³ + 10 xy² - 24 x²y + 8 x³ = 0

⇒ ( 2 x - 3 y )³ + 2 ( 6 y³ + 5 xy² - 12 x²y + 4 x³ ) = 0

⇒ ( 2 x - 3 y )³ + 2 ( 4 x³ - 12 x²y + 5 xy² + 6 y³ ) = 0

⇒ ( 2 x - 3 y )³ + 2 ( 4 x³ + 2 x²y - 8 x²y - 4 xy² - 6 x²y - 3 xy² + 12 xy² + 6 y³ ) = 0

⇒ ( 2 x - 3 y )³ + 2 [ 2 x ( 2 x² + x y - 4 xy - 2 y ) - 3 ( 2 x² + x y - 4 xy - 2 y ) ] = 0

⇒ ( 2 x - 3 y )³ + 2 ( 2 x - 3 y )( 2 x² + x y - 4 xy - 2 y ) = 0

⇒ ( 2 x - 3 y )³ + 2 ( 2 x - 3 y )( x (2 x + y) - 2(2 x + y) ) = 0

⇒ ( 2 x - 3 y )³ + 2 ( 2 x - 3 y )( x - 2 )( 2 x + y ) = 0

⇒ ( 2 x - 3 y ) [ ( 2 x - 3 y )² + 2 ( x - 2 )( 2 x + y ) ] = 0

The only whole number ratio solution possible over here is 2 x - 3 y = 0 ⇒ 2 x = 3 y ⇒ x : y = 3 : 2

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Answer 2

Answer:

3 is to 2

Step-by-step explanation: