Crazy Numbers!

Algebra Level pending

If N= 123456789 × 765432110 + 2345678 9 2 123456789 \times 765432110 + 23456789^{2} then find N

1 0 8 10^{8} 1 0 16 10^{16} 1 0 32 10^{32} 1 0 9 10^{9}

Sriharsha Ch by Sriharsha Ch , 20, India

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1 solution

Sriharsha Ch
May 23, 2015

N= ( 1 0 8 + 23456789 ) × 76543211 + ( 23456789 ) 2 (10^{8} + 23456789) \times 76543211 + (23456789)^{2}

= 76543211 × 1 0 8 + 76543211 × 23456789 + 2345678 9 2 76543211 \times 10^{8} + 76543211 \times 23456789 + 23456789^{2}

= 1 0 8 × 76543211 + 23456789 × ( 76543211 + 23456789 ) 10^{8} \times 76543211 + 23456789 \times (76543211+23456789)

= 1 0 8 × 76543211 + 1 0 8 × 23456789 10^{8} \times 76543211 + 10^{8} \times 23456789

= 1 0 8 × ( 76543211 + 23456789 ) 10^{8} \times (76543211+23456789)

= 1 0 8 × 1 0 8 10^{8} \times 10^{8}

= 1 0 16 10^{16}

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