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lana [24]
3 years ago
15

The product of two number is 20 and the sum of square is 41 find the number​

Mathematics
2 answers:
Marianna [84]3 years ago
6 0

Let the two number is a and b

so,

product =ab=20

sum of square=\bold{a^2+b^2=41   }

Then,

\bold{(a+b)^2=a^2+b^2+2ab  }

\bold{ (a+b)^2=41+2×40  }

\bold{ (a+b)^2=81  }

\bold{a+b=\sqrt{81}   }

\bold{a+b=9 }•••••••••(equation I)

Now,

\bold{(a-b)^2=a^2+b^2-4ab   }

\bold{ (a-b)^2=41-4×20  }

\bold{(a-b)^2=41-40   }

\bold{a-b=\sqrt{1}   }

\bold{a-b=1 }••••••••(equation II)

Now,combine the equation I and equation II

we,get

\bold{a+b+a-b=9+1   }

\bold{a+\cancel{b}+a\cancel{-b}=10   }

\bold{ 2a=10  }

\bold{a=\dfrac{10}{2}   }

\blue{\boxed{  a=5 }}

Then,

put the value of a in equation II.

we get that,

\bold{5-b=1   }

\bold{b+1=5   }

\bold{b=5-1   }

\bold{\boxed{\blue{b=4}}  }

<em><u>so</u></em><em><u>,</u></em><em><u> </u></em>

<em><u>The</u></em><em><u> </u></em><em><u>two</u></em><em><u> </u></em><em><u>number</u></em><em><u> </u></em><em><u>is</u></em><em><u> </u></em><em><u> </u></em><em><u>5</u></em><em><u> </u></em><em><u>and</u></em><em><u> </u></em><em><u>4</u></em><em><u>.</u></em>

larisa [96]3 years ago
5 0

Answer:

The numbers are 4 and 5. Their sum = 25 + 16 = 41.

Step-by-step explanation:

Hope this helped :3

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