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प्रश्न
Simplify:
\[\frac{a^3 - 27}{5 a^2 - 16a + 3} \div \frac{a^2 + 3a + 9}{25 a^2 - 1}\]
उत्तर
It is known that,
a2 − b2 = (a + b) (a − b)
a3 − b3 = (a − b)(a2 + ab + b2)
\[\ \frac{a^3 - 27}{5 a^2 - 16a + 3} \div \frac{a^2 + 3a + 9}{25 a^2 - 1}\]
\[ = \frac{\left( a \right)^3 - \left(3 \right)^3}{5 a^2 - 15a - a + 3} \div \frac{a^2 + 3a + 9}{\left( 5a \right)^2 - \left( 1 \right)^2}\]
\[ = \frac{\left(a - 3 \right)\left\{ \left( a \right)^2 + \left(a \right) \times \left(3 \right) + \left(3 \right)^2 \right\}}{5a\left(a - 3 \right) - 1\left( a - 3 \right)} \div \frac{a^2 + 3a + 9}{\left(5a + 1 \right)\left(5a - 1 \right)}\]
\[ = \frac{\left(a - 3 \right)\left(a^2 + 3a + 9 \right)}{\left(5a - 1 \right)\left(a - 3 \right)} \div \frac{\left( a^2 + 3a + 9 \right)}{\left(5a + 1 \right)\left(5a - 1 \right)}\]
\[ = \frac{\left(a - 3 \right)\left(a^2 + 3a + 9 \right)}{\left(5a - 1 \right)\left(a - 3 \right)} \times \frac{\left(5a + 1 \right)\left(5a - 1 \right)}{\left(a^2 + 3a + 9 \right)}\]
\[ = 5a + 1\]
संबंधित प्रश्न
Simplify:
\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]
Factorise:
x3 − 64y3
Factorise:
125y3 − 1
Factorise:
8p3 −\[\frac{27}{p^3}\]
Simplify:
(3a + 5b)3 − (3a − 5b)3
Simplify:
(a + b)3 − a3 − b3
Factorise: 27p3 - 125q3.
Factorise: `a^3 - 1/(a^3)`
Simplify: (2x + 3y)3 - (2x - 3y)3
Factorise the following:
27x3 – 8y3
