Question

solve: 49³-30³+(...........)³= 3 × 49 × 30 × 19​

Answer 1

SOLUTION

TO FILL IN THE BLANK

49³ - 30³ + ( _____ )³= 3 × 49 × 30 × 19

EVALUATION

We are aware of the formula that

$\sf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y)}$

Take x = 49 & y = 19 so that above becomes

$\sf{ {(49 - 19)}^{3} = {49}^{3} - {19}^{3} - 3 \times 49 \times 19 \times (49- 19)}$

$\sf{ \implies {30}^{3} = {49}^{3} - {19}^{3} - 3 \times 49 \times 19 \times 30}$

$\sf{ \implies {19}^{3} = {49}^{3} - {30}^{3} - 3 \times 49 \times 19 \times 30}$

$\sf{ \implies {49}^{3} - {30}^{3} - {19}^{3} = 3 \times 49 \times 19 \times 30}$

$\sf{ \implies {49}^{3} - {30}^{3} + {( - 19)}^{3} = 3 \times 49 \times 30 \times 19}$

FINAL ANSWER

$\sf{ \implies {49}^{3} - {30}^{3} + \underline{{( - 19)}^{3}} = 3 \times 49 \times 30 \times 19}$

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