Prove that 59-59 - 59-9 - 9 - 9-59- 59 - 59 - 9-9-9- 50-

ANSWER: 59×59 × 59 9 × 9 × 9/59× 59 + 59 × 9+9×9 = (59^3 9^3)/59^2+59×9+9^2 We know a^3+b^3=(a+b)(a^2+b^2 ab) Here a=59,b=9 So,(59 9)(59^2+9^2+59×9)/59^2+9^2+59 ...

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Standard VIII

Mathematics

Factorisation Using Algebraic Identities

Prove that 59...

Question

Prove that $\frac{59 \times 59 \times 59 - 9 \times 9 \times 9}{59 \times 59 + 59 \times 9 + 9 \times 9} = 50.$

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Solution

ANSWER:
$\frac{59 \times 59 \times 59 - 9 \times 9 \times 9}{59 \times 59 + 59 \times 9 + 9 \times 9}$
$= \frac{(59^{3} - 9^{3})}{59^{2} + 59 \times 9 + 9^{2}}$
We know $a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)$
Here
a=59,b=9
So, $\frac{(59 - 9) (59^{2} + 9^{2} + 59 \times 9)}{59^{2} + 9^{2} + 59 \times 9} = 59 - 9 = 50 : R H S$

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Prove that 59×59×59−9×9×959×59+59×9+9×9=50.

ANSWER: 59×59×59−9×9×959×59+59×9+9×9 =(593−93)592+59×9+92 We know a3+b3=(a+b)(a2+b2−ab) Here a=59,b=9 So,(59−9)(592+92+59×9)592+92+59×9=59−9=50 :RHS

Prove that $\frac{59 \times 59 \times 59 - 9 \times 9 \times 9}{59 \times 59 + 59 \times 9 + 9 \times 9} = 50.$