Can someone send me the answers of these questions... Don't spam...
Answers
Solution :
27. Let us assume that √2 is a rational number.
√2 = p/q , q ≠ 0 and (p,q) = 1
Squaring both sides -
2 = p²/q²
=> p² = 2q²
=> q² = p²/2 and p is integral ; so p is an even number.
Let p = 2k
=> q² = ( 4k² )/2
=> k² = q²/2 , and q is integral.
So, this means that both p and q are even , but ( p, q ) = 1.
Hence , by contradiction √2 is irrational .
28.
x² + 5x - ( a² + a - 6 ) = 0
=> x² + 5x - ( a² + 3a - 2a - 6) = 0
=> x² + 5x - ( a( a + 3) - 2( a + 3) ) = 0
=> x² + 5x - ( a + 3)( a - 2) = 0
=> x² + [ ( a + 3) - ( a - 2) ] x - ( a + 3)( a - 2) = 0
=> x² + ( a + 3)x - ( a - 2)x - (a + 3)( a - 2) = 0
=>x [x + a + 3 ] - ( a - 2) [ x + a + 3 ] = 0
=> [ x + a + 3 ][ x - a + 2 ] = 0
[ OR ]
Ths numerator of the fraction is one less than its denominator.
Let the denominator be x .
The faction becomes ( x - 1)/x
3 is added to both the numerator & denominator
=> ( x + 2)/( x + 3) = ( x - 1)/x + 3/28
=> ( x + 2)/(x + 3) - ( x - 1)/x = 3/28
=> [ ( x + 2)x - ( x - 1)( x + 3) ]/[ x( x + 3)] = 3/28
=> [ x² + 2x - ( x² + 2x - 3 ) ]/[ x(x+3) ] = 3/28
=> 3/[ x(x + 3)] = 3/28
=> x( x + 3) = 28
=> x² + 3x = 28
=> x² + 3x - 28 = 0
=> x² + 7x - 4x - 28 = 0
=> x( x + 7) - 4( x + 7) = 0
=> ( x - 4)( x + 7) = 0
x = 4
The required fraction becomes ¾ .
_____________________________________________
This is the required solution.
Please mark me as the brainliest answer
