13) The volume of a cube is given by polynomial p(x)=8x3-36x2+54x-27. Find the possible expression for the side of the cube .Verify it when side of the cube is 3cm .
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Given, p(x ) =8x³-36x²+54x - 27
This is in the form of ( a - b)³
(2x)³+(-3)³-3(2x)(3)(2x-3)
= 8x³-27-36x²+54x.
Hence, The expression for the side of cube = ( 2x - 3 )
When, the side of cube = 3 then ,
2x -3 = 3
2x = 6 .
x = 3 .
Volume of cube = 8(27)-36(9)+54(3)-27 = 216-324+162-27 = 27 cm³ .
We can find the same by Volume = 3³ = 27 cm³
This is in the form of ( a - b)³
(2x)³+(-3)³-3(2x)(3)(2x-3)
= 8x³-27-36x²+54x.
Hence, The expression for the side of cube = ( 2x - 3 )
When, the side of cube = 3 then ,
2x -3 = 3
2x = 6 .
x = 3 .
Volume of cube = 8(27)-36(9)+54(3)-27 = 216-324+162-27 = 27 cm³ .
We can find the same by Volume = 3³ = 27 cm³
Answered by
0
Answer:
Step-by-step explanation:Given, p(x ) =8x³-36x²+54x - 27
This is in the form of ( a - b)³
(2x)³+(-3)³-3(2x)(3)(2x-3)
= 8x³-27-36x²+54x.
Hence, The expression for the side of cube = ( 2x - 3 )
When, the side of cube = 3 then ,
2x -3 = 3
2x = 6 .
x = 3 .
Volume of cube = 8(27)-36(9)+54(3)-27 = 216-324+162-27 = 27 cm³ .
We can find the same by Volume = 3³ = 27 cm³
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