x³-2x²y-y³,7x²y-4x³ and 4y³+5x²y simplify
Answers
Answer:
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 .
ANSWER : OPTION B
Step-by-step explanation:
Go on splitting your whole life until the half part of the equation becomes equivalent to x³ + 3 x²y + 3 xy² + y³ + something = 0 . Now you know that the left part is (x+y)³ and on further splitting on the right part the solution can be factored . I think I have done in the lengthiest method possible . If I get time , I will think of an easier alternative method .
Step-by-step explanation:
Answer:
-3x³+10x²y+3y³
Step-by-step explanation:
= x³-2x²y-y³+7x²y-4x³+4y³+5x²y
= x³-4x³-2x²y+7x²y+5x²y-y³+4y³
= -3x³-2x²y+12x²y+3y³
= -3x³+10x²y+3y³