Question

is the following possible? the sum of ages of a mother and her daughter is 25 years . Five year ago the product of their ages was 58

Answer 1

Let the present age of mother and her daughter be x and y respectively.

Now,

According to the question,

◉ Sum of ages of mother and her daughter = 25

⇒ x + y = 25

∴ x = 25 - y ...(1)

Also,

◉ Five years ago product of thier ages = 58

⇒ (x - 5) × (y - 5) = 58

Substitute x = 25 - y { from (1) }

⇒ (25 - y - 5)(y - 5) = 58

⇒ (20 - y)(y - 5) = 58

⇒ 20y - 100 - y² + 5y = 58

⇒ 25y - y² = 158

⇒ y² - 25y + 158 = 0

Here, Let's find the discriminant to know if the age of daughter would be a real number.

D = b² - 4ac

Comparing the given quadratic equation with the standard form of quadratic equation ( i.e., ax² + bx + c = 0) , we get

• a = 1
• b = -25
• c = 158

⇒ D = (-25)² - 4×1×158

⇒ D = 625 - 632

⇒ D = -7

Here, Discriminant D is less than 0, So No real value is possible, Hence this situation is not possible.

Some Information :-

◉ The standard form of quadratic equation is ax² + bx + c = 0, Where, a≠0 and b & c are constants.

◉ The discriminant D = b² - 4ac, If

• Negative or D < 0

⇒ No Real root exists, But imaginary roots satisfy the equation.

• Equal to 0 or D = 0

⇒ Two real and equal roots exist.

• Positive or D > 0

⇒ Two real and distinct roots exist.

Answer 2

Answer:

I hope this answer will help you.