Question

Find the roots x²-4√7x-35 =0

Answer 1

$Given \: Quadratic\: Equation :\\x^{2} - 4\sqrt{7}x - 35 = 0$

/* Splitting the middle term, we get */

$\implies x^{2} + \sqrt{7}x - 5\sqrt{7}x - 35 = 0$

$\implies x( x + \sqrt{7}) - 5\sqrt{7}( x + \sqrt{7}) = 0$

$\implies (x+\sqrt{7}) (x-5\sqrt{7}) = 0$

$\implies x+\sqrt{7}= 0 \: Or \:x-5\sqrt{7}= 0$

$\implies x = -\sqrt{7} \: Or \:x = 5\sqrt{7}$

Therefore.,

$\green{ x = -\sqrt{7} \: Or \:x = 5\sqrt{7} }$

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Answer 2

Answer:By completing square method

Step-by-step explanation:

x²-4√7x=35

Dividing both sides by 1

x²-4√7x=35 (a²-2ab+b²)

(x)²-2(x)(2√7)+(2√7)²-(2√7)²=35

(x-2√7)²-(2√7)²=35

(x-2√7)²=35+(2√7)²

(x-2√7)²=35+28

x-2√7=±√63

First take positive

x=√63+2√7

x=2√70

Second take negative

x=√63-2√7

x=2√56=>8√6

So the roots of x²-4√7x-35=0 are x=2√70 and x=8√56