What is the best solution of exercise 4.4 of quadratic equation of ncert class 10th math. This is very important type of question for board exam Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48

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# Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.Q.4

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Letâ€™s say, the age of one friend be x years.

Then, the age of the other friend will be (20 â€“ x) years.

Four years ago,

Age of First friend = (

xÂ â€“ 4) yearsAge of Second friend = (20 â€“Â

xÂ â€“ 4)Â = (16 â€“Â x) yearsAs per the given question, we can write,

(

xÂ â€“ 4) (16 â€“Âx) = 4816

x â€“ x^{2}Â â€“ 64 + 4xÂ = 48Â â€“ x^{2}Â +Â 20x â€“Â112 = 0x^{2}Â â€“Â 20x +Â112 = 0Comparing the equation withÂ

ax^{2}Â +ÂbxÂ+ÂcÂ = 0, we getaÂ =Â1,ÂbÂ = -20Â andÂcÂ = 112Discriminant =Â

b^{2}Â â€“ 4ac= (-20)^{2}Â â€“ 4 Ã— 112= 400 â€“ 448 = -48

b^{2}Â â€“ 4acÂ< 0Therefore, there will be no real solution possible for the equations. Hence, condition doesnâ€™t exist.