FIND TWO NUMBER WHOSE SUM IS 27 AND PRODUCT IS 182 (EX. 4.2 Q.(3) CLASS 10TH MATHS NCERT SOLUTION)
प्रश्न -(3) ऐसी दो संख्याये ज्ञात कीजिये। जिनका योग 27 और गुणनफल 182 हो।
हल : माना की एक संख्या X हे , तो दूसरी संख्या 27 -X होगी।
अब प्रश्नानुसार , X (27 -X ) = 182
=> 27X - X^2 =182
=> -X^2 +27X -182 =0
(-) चिन्ह से गुणा करने पर,
=> X^2 -27X +182 =0
=> X^ 2 -13X -14X +182 =0
=> X (X -13 ) -14 (X -13 ) =0
=> ( X -13 )(X -14 )=0
=> X -13 =0 => X =13
=> X -14 =0 => X =14
चूँकि 13 और 14 का योग 27 हे और गुणनफल 182 हे। अभीष्ट संख्या 13 और 14 हे।
ENGLISH TRANSLATION :
Question-(3) Find two such numbers. Whose sum is 27 and product is 182.
Solution : Let one number be X, then the other number will be 27 -X.
Now according to the question, X (27 -X ) = 182
=> 27X - X^2 =182
=> -X^2 +27X-182 =0
(-) on multiplying by the sign,
=> X^2 -27X +182 =0
=> X^ 2 -13X -14X +182 =0
=> X (X -13 ) -14 (X -13 ) =0
=> ( X -13 )(X -14 )=0
=> X -13 =0 => X =13
=> X -14 =0 => X =14
Since the sum of 13 and 14 is 27 and the product is 182. Required numbers are 13 and 14.