If Ahana were 5 years younger than what she really is, then square of her age would have been one year more than four times her present age what is her present age ?
Answers
Answer:
Let x= Zeba’s present actual age
In the question it is given that,
Zeba were younger by 5 years than what she really, can be write in expression as (x - 5) years
Square of her age i.e.squareof(x−5) would have been 11 more than five times her actual age (x)
equation can be formed as
⇒(x - 5)2=11 + 5x ( Using(a - b)2=a2+b2−2ab) here, a = x and b = 5
⇒x2+25−10x=11 + 5x
On arranging one side and forming quadratic equation
⇒x2+25−10x−5x - 11=0
⇒x2−15x+14=0
We have, a quadratic equation x2−15x+14=0
Sridharacharya formula is actually the quadratic formula, used for finding the roots of a quadratic equation ax2 + bx + c = 0
, where a not equal to 0 , & a, b, c are real coefficients of the equation ax2 + bx + c = 0
Being quadratic it has 2 roots.
⇒X = (−b + b2−4ac−−−−−−−√)2a & (−b - b2−4ac−−−−−−−√)2a (1)
On comparing the given equation x2−15x+14=0 with the general quadratic equation ax2 + bx + c = 0
we got values of coefficients a = 1, b = -15, c = 14
On putting the value of coefficients a, b, c in equation (1)
⇒x = (−(−15) + (−15)2−4×(1)×(14)−−−−−−−−−−−−−−−−−−−√)2×1 & (−(−15) - (−15)2−4×(1)×(14)−−−−−−−−−−−−−−−−−−−√)2×1
⇒x = (15 + 225−56−−−−−−−√)2 & (15 - 225−56−−−−−−−√)2
⇒x = (15 + 169−−−√)2 & (15 - 169−−−√)2
⇒x = (15 + 13)2 & (15 - 13)2
⇒x = 282 = 14, & 22=1
⇒x1 = 14 & x2 = 1
Since her age can't be 1, So it is 14.
Zeba’s present actual age=14
Note: In such types of particular questions, we got two roots from the quadratic equation formed by the given condition in the question. Here, sometimes both roots are the correct answer and sometimes only one root we select as a correct answer. It depends on roots whether they are satisfying the given condition given in the question or not. If both roots satisfied the given conditions, then both will be selected as the correct answer. For example- In the above question, for x=1,
When Zeba was younger by 5 years, then her age can be expressed as (x - 5) i.e. (1-5) = - 4, which is a negative quantity and Age can’t be negative, hence x=1 can’t be the right answer.
Step-by-step explanation:
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