Question

solve each of the following equations i) √2 x^ 2+ x+√2 =0 ii) x^ 2+3x+5=0​

Answer 1

$\bigstar \: \boxed{\sf{\color{purple}{Answer:}}}$

i) x 2−3x−10=0

⇒x 2−5x+2x−10=0

⇒x(x−5)+2(x−5)=0

⇒(x+2)(x−5)=0

⇒x=5,−2

ii)

2x 2+x−6=0⇒2x 2

+4x−3x−6=0

⇒2x(x+2)−3(x+2)=0

⇒(x+2)(2x−3)=0

⇒x= 23,−2

iii)

2 x 2+7x+5 2=0⇒ 2 x 2

+2x+5x+5 2=0

⇒ 2

x(x+ 2 )+5(x+ 2 )=)

⇒(x+ 2 )( 2 x+5)=0

⇒x=− 2, 2−5

iv)

2x 2 −x+ 81 =0

⇒16x 2−8x+1=0

⇒16x 2 −4x−4x+1=0

⇒16x(x− 41)−4(x− 41 )=0

⇒(x− 41 )(16x−4)=0⇒x= 41 , 41

v) 100x 2

−20x+1=0

⇒100x 2

−10x−10x+1=0

⇒10x(10x−1)−1(10x−1)=0

⇒(10x−1)(10x−1)=0

⇒x= 101 , 101

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