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1. If x>y>0, x^2+y^2=13 and xy=6, then y=?
2. Solve by factorrization method 4x^2-4ax+(a^2-b^2)=0 (a,b,E R).
3. If the price of a book is reduced by Rs. 5 a person can buy 5 more books for Rs. 300. Find the original price of the book?
4. A 2-digit number is four times the sum and the three times the product of its digit. Find the number?
5. The sum of the squares of two consecutive odd number is 394. Find the numbers?
SOLUTION FOR QUESTION NO.-1
Since it is given that x>y>0 & 2x=2y=13
=>2(x+y)=13
=>x+y=13/2-(1)
Since it is also given that xy=6 =>y=x/6
putting the value of y in (1):-
x+6/x=13/2
2xsq+12=13x
2xsq-13x+12=0
x=13+_under root(73)
----------------------- >0
4
now, putting the value of y in (2) we get:-
y=24
--------------------- >0
13+_under root(73)
SOLUTION FOR QUESTION NO.-5
Let 1 odd no. be x & its consequtive be (x+2)
since sum of their squares=394
Therefore,
A/Q :-
xsq. + (x+2)sq.=394
xsq.+xsq.+4+4x=394
2xsq.+4x-390=0
xsq.+2x-195=0
On using the quadratic formula, we get:-
x=-2+_under root(784)
______________________
2
=28-2 or -28-2
____ _______
2 2
= 13 or -15
Therefore now
the req. 2 nos are:-
13 & (13+2) or -15 & (-15+2)
13 and 15 or -15 and -13
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