Q. If x+y+z=0, show that x³+y³+z³=3xyz.
Sol:
Given,
=>x+ y+ z=0
=>x+ y = - z_______(1)
=>(x+y)³=( - z)³
=>x³+y³ - 3xy(x+y)= - z³
=>x3+y³ - 3xy( - z)= - z³ [from eqn (1)]
=>x³+y³ - 3xyz= - z³
=>x³+y³+z³=3xyz
__
Q. Express 4.035 in the form of p/q.
Sol: __
Let, x=4.035
=> x = 4.0353535........
=>10x=40.353535......._____(1)
=>1000x=4035.3535.....____(2)
So, (2) - (1)
=>990x=3995
=> x = 3995/990
=> x = 799/198
Q. Find the perimeter of a isosceles triangle whose base measure is 24cm and area is 60cm².
Sol:
Let, each equal sides of the triangle be 'x' cm
i.e.,
s=(x+x+24)/2
=>s=(2x+24)/2
=>s=2x/2+24/2
=>s=x + 12
Area=√(x+12)(x+12 - x)(x+12 - x)(x+12 - 24)
=> 60 = √(x+12)(12)(12)(x-12)
=> 60 = 12√(x² - 12²)
=> 5 =√(x² - 144)
=>25=x² - 144
=>25+144=x²
=>169=x²
=> 13²=x²
=> 13=x
P=13+13+24
=50
Hence perimeter of the given triangle is 50cm.
