Math, asked by shreyabambal, 1 year ago

Find (64x)cube - (125z)cube if 4x -5z =16,xz=12

Answers

Answered by hukam0685

153

$64 {x}^{3} - 125 {z}^{3} = ( {4x)}^{3} - ( {5z)}^{3} \\ = (4x - 5z)( 16{x}^{2} + 20xz + 25{z}^{2}+40xz-40xz ). to make it square \\ = 16(( {4x - 5z)}^{2} + 60xz) \\ = 16( {16}^{2} + 60 \times 12) \\ = 16(256 + 720) \\ = 16 \times 976 \\ = 15616$

shreyabambal: I checked it's correct

shreyabambal: Answer is 15616

hukam0685: ok i will check it again

hukam0685: i had made the corrections,while making square i had made a mistake,hope you understand

shreyabambal: Yes

hukam0685: by my method,hope you understand,what i had did

shreyabambal: From where 40xz came

hukam0685: i had add and subtract 40 xz to make it perfect square of (4x-5z),i think you should slide your screen to see it full

shreyabambal: Okay

shreyabambal: Thanks

Answered by ishanaghosh

64x^3-125z^3
=(4x)^3-(5z)^3
=(4x-5z)^3+3×4x×5z(4x-5z)
=16^3+60×12×16
=4096+11520
=15616 ans.

shreyabambal: I didn't understood

shreyabambal: Thanks

shreyabambal: For explaining

ishanaghosh: We have used the formula a^3-b^3=(a-b)^3-3ab(a-b)

ishanaghosh: In the question (a-b) value was given and so this formula had to be used.

ishanaghosh: In the question, we see that the cubes of 4 & 5 are there and so we convert to the form a^3-b^3

ishanaghosh: Then we put the formula and calculate.

ishanaghosh: Then we put the values.

ishanaghosh: After + in step 3 I have multiplied 3,4 of 4x and 5 of 5z to get 60, put the value of xz to get 12 and put the value of the bracketed portion to get 16.

ishanaghosh: I hope it is clear now. If not, you are free to ask again.

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