Math, asked by cwalia162, 8 months ago

evolute (997)3 using identity​

Answers

Answered by amankumaraman11
2

Here are some identities useful in solving Question like above (one) :

 \bullet \:  \rm(x + y)(x + y) =   {x}^{2}  + 2xy +  {y}^{2}\\ \bullet \: \rm (x - y)(x - y)  =  {x}^{2} - 2xy +  {y}^{2}   \\  \small\bullet \:  \rm (x + a)(x + b)  =  {(x)}^{2} + (a + b)x + ab \\ \bullet \: \rm (x - y)(x + y) =  {(x)}^{2}  -  {(y)}^{2}  \\   \small\bullet \:  \rm(x + y)(x + y)(x + y) =  {x}^{3}  +  {y}^{3}  +  {3x}^{2} y  + {3xy}^{2}  \\ \small\bullet \:  \rm(x - y)(x - y)(x - y) =  {x}^{3}  -  {y}^{3}  - 3xy(x - y)

Now,

▪Simplifying the (given) expression as :

 \tt \huge \mapsto \:  \:  \:  {(997)}^{3}  \\  \ \\ \huge  \mapsto  \: \:  \sf( {1000 - 3)}^{3}  \\   \\  \small  \to \:  \sf {(1000)}^{3}  -  {(3)}^{3}  - 3(1000)(3) \{ 1000 - 3\} \\    \to \:  \sf 1000000000  - 27 - 9000  \{ 1000 - 3\} \\  \to \:  \sf 1000000000  - 27 - 9000000 + 27000  \\  \small \to \:  \sf1000027000  - 9000027 \\  \to \:  \sf  \red{ 991026973}

Hence,

  • \tt {(997)}^{3}  =  \red{991026973}
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