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ืžื™ื“ืข ืขืœ ื”ืืคืœื™ืงืฆื™ื” ื”ื–ื•

ืžื—ืฉื‘ื•ืŸ ืžืชืžื˜ื™ืงื” ื—ื™ื ืžื™ ื–ื” ื™ืคืชื•ืจ ื‘ืื•ืคืŸ ืžื™ื™ื“ื™ ืืช ืžืฉื•ื•ืืช ื”ืคื™ืชื’ื•ืจืก, ืฉืœืฉื•ืช ืคื™ืชื’ื•ืจื™ื•ืช, ื–ื”ื•ื™ื•ืช ืคื™ืชื’ื•ืจื™ื•ืช, ื ื•ืกื—ืช ืžืฉืคื˜ ืคื™ืชื’ื•ืจืก, ื”ื•ื›ื—ืช ืžืฉืคื˜ ืคื™ืชื’ื•ืจืก,
ืคื™ืชื’ื•ืจืก ื•ื—ื•ืกืจ ืฉื•ื•ื™ื•ืŸ ื‘ืคื™ืชื’ื•ืจืก.

ืžืฉืคื˜ ืคื™ืชื’ื•ืจืก ืงื•ื‘ืข ื›ื™ aยฒ + bยฒ = cยฒ. ื”ืืคืœื™ืงืฆื™ื” ืชื—ืฉื‘ ืืช ื”ืฆื“ ื”ืฉืœื™ืฉื™ ืขืœ ืคื™ ืžืฉืคื˜ ืคื™ืชื’ื•ืจืก.

ืœื“ื•ื’ืžื” ื”ื–ืŸ ืฆื“ A ื•ืืช ื”ืฆื“ื“ื™ื B ื•ื”ืžื—ืฉื‘ื•ืŸ ื™ื—ืฉื‘ ืืช ืื•ืจืš ื”ืฆื“ C.

ื”ืืคืœื™ืงืฆื™ื” ื”ื˜ื•ื‘ื” ื‘ื™ื•ืชืจ ืœื‘ื™ืช ื”ืกืคืจ ื•ื”ืžื›ืœืœื”! ืื ืืชื” ืกื˜ื•ื“ื ื˜, ื–ื” ื™ืขื–ื•ืจ ืœืš ืœืœืžื•ื“ ืืœื’ื‘ืจื” ื•ื’ื™ืื•ืžื˜ืจื™ื”!
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ืื‘ื˜ื—ืช ื ืชื•ื ื™ื

ื›ื“ื™ ืœืฉืžื•ืจ ืขืœ ื”ื‘ื˜ื™ื—ื•ืช ืฆืจื™ืš ืงื•ื“ื ื›ืœ ืœื”ื‘ื™ืŸ ืื™ืš ื”ืžืคืชื—ื™ื ืื•ืกืคื™ื ื•ืžืฉืชืคื™ื ืืช ื”ื ืชื•ื ื™ื ืฉืœืš. ื ื•ื”ืœื™ ืคืจื˜ื™ื•ืช ื”ื ืชื•ื ื™ื ื•ืื‘ื˜ื—ืช ื”ื ืชื•ื ื™ื ืขืฉื•ื™ื™ื ืœื”ืฉืชื ื•ืช ื‘ื”ืชืื ืœืฉื™ืžื•ืฉ, ืœืื–ื•ืจ ื•ืœื’ื™ืœ ื”ืžืฉืชืžืฉ. ื”ืžืคืชื— ืกื™ืคืง ืืช ื”ืžื™ื“ืข ื”ื–ื” ื•ื”ื•ื ืขืฉื•ื™ ืœืขื“ื›ืŸ ืื•ืชื• ืžื“ื™ ืคืขื.
ืœื ืžืชื‘ืฆืข ืฉื™ืชื•ืฃ ื ืชื•ื ื™ื ืขื ืฆื“ื“ื™ื ืฉืœื™ืฉื™ื™ื
ื”ืืคืœื™ืงืฆื™ื” ื”ื–ืืช ืขืฉื•ื™ื” ืœืืกื•ืฃ ืืช ืกื•ื’ื™ ื”ื ืชื•ื ื™ื ื”ืืœื”
ืžื™ื“ืข ืขืœ ื”ืืคืœื™ืงืฆื™ื” ื•ื‘ื™ืฆื•ืขื™ ื”ืืคืœื™ืงืฆื™ื” ื•ืžื–ื”ื” ื”ืžื›ืฉื™ืจ ืื• ืžื–ื”ื™ื ืื—ืจื™ื
ื”ื ืชื•ื ื™ื ืžื•ืฆืคื ื™ื ื‘ื–ืžืŸ ื”ื”ืขื‘ืจื”
ืื™ ืืคืฉืจ ืœืžื—ื•ืง ืืช ื”ื ืชื•ื ื™ื

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ืชืžื™ื›ื” ื‘ืืคืœื™ืงืฆื™ื”

ืžื™ื“ืข ืขืœ ืžืคืชื—ื™ ื”ืืคืœื™ืงืฆื™ื”
Ahmad Javaid
mathematicsapps@gmail.com
House no 78-C , Canal Bank Extension Lahore, 54000 Pakistan

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