Respuesta :
Answer:
Asha's present age is 27 years and Nisha's present age is 5 years.
Step-by-step explanation:
Let the present age of Nisha be [tex]x[/tex] years.
As per question, Asha's present age is 2 more than the square of Nisha's age.
[tex]\therefore[/tex] Asha's present age = [tex]x^2+2[/tex]
Now, Nisha will reach her mother's age after [tex]x^2+2-x[/tex] years.
Therefore, age of Asha after [tex]x^2+2-x[/tex] years will be = [tex]x^2+2+x^2+2-x=2x^2-x+4[/tex]
Now, as per question,
[tex]2x^2-x+4=10x-1\\2x^2-x-10x+4+1=0\\2x^2-11x+5=0\\2x^2-x-10x+5=0\\x(2x-1)-5(2x-1)=0\\(2x-1)(x-5)=0\\x=\frac{1}{2}\ or\ x=5[/tex]
As age can't be in fraction, we consider the present age of Nisha as 5 years. So, Asha's present age is [tex]x^2+2=5^2+2=25+2=27[/tex] years.
Therefore, Asha's present age is 27 years and Nisha's present age is 5 years.
