Question

And this one too?

I need explanation for your answers, how did u get it.

*no explanation report* respect :)

Brainliest Answer for those who'll answer this questions properly.. ​

Answer 1

Answer:

1. a.

2. a.

3. c.

4. a

5. a.

Step-by-step explanation:

1. a perfect square trinomial is a square of a binomial.

${x}^{2} + 10x + 25 = {x}^{2} + 5x + 5x + 25 \\ = x(x + 5) + 5(x + 5) \\ = (x + 5)(x + 5) = {(x + 5)}^{2}$

where x + 5 is a binomial and given equation is a square of a binomial.

2.

${x}^{2} - 7x + 12 = {x}^{2} - 3x - 4x + 12 \\ = x(x - 3) - 4(x - 3) \\ = (x - 4)(x - 3)$

for which x, the above binomial becomes 0 then the equation will be the roots and those numbers are 3 and 4.

3. to solve an equation easily by extracting square roots the equation must be in the form of a^2 = b or a^2 - b = 0

where option c is exactly in this form I.e, x^2 - 64 = 0 which means x^2 = 64 so, x = (+ or -) square root of 64 = 8 or -8.

4.

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}$

R.H.S is the perfect square trinomial in above equation.

${x}^{2} + 12x = {x}^{2} + 2 \times 6 \times x \\ here \: {y}^{2} term \: is \: missing \: and \: 6 = y \\ then \: {y}^{2} = {6}^{2} = 36$

so, 36 has to be added to get perfect square trinomial.

5.

${x}^{2} + 5x + 6 = 0 \\ {x }^{2} + 2x + 3x + 6 = 0 \\ x(x + 2) + 3(x + 2) = 0 \\ (x + 3)(x + 2) = 0$

so x = -2 or x = -3 are the roots for above equation.