Question

Solve for y 16y^2-25=0

Answer 1

The value of y is 5/4 or -5/4

Step-by-step explanation:

16y² - 25 = 0

This is a quadratic equation in y

16y² = 25

(4y)² = 5²

Taking square root on both the sides yields;

√(4y)² = √5²

4y = ± 5

Dividing both sides by 4 yields; y =5/4 or y= -5/4

Answer 2

`\large\boxed{x=-(5)/(4)\ \vee\ x=(5)/(4)}`

Explanation:

`16y^2-25=0\\\\METHOD\ 1:\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\16=4^2\ \text{and}\ 25=5^2\ \text{therefore we have}\\\\4^2y^2-5^2=0\\\\(4y)^2-5^2=0\\\\(4y-5)(4y+5)+0\iff4y-5=0\ \vee\ 4y+5=0\\\\4y-5=0\qquad\text{add 5 to both sides}\\4y=5\qquad\text{divide both sides by 4}\\\boxed{y=(5)/(4)}\\\\4y+5=0\qquad\text{subtract 5 from both sides}\\4y=-5\qquad\text{divide both sides by 4}\\\boxed{x=-(5)/(4)}`

`METHOD\ 2:\\\\16y^2-25=0\qquad\text{add 25 to both sides}\\\\16y^2=25\qquad\text{divide both sides by 16}\\\\y^2=(25)/(16)\to y=\pm\sqrt{(25)/(26)}\\\\y=-(√(25))/(√(16))\ \vee\ x=(√(25))/(√(16))\\\\\boxed{y=-(5)/(4)\ \vee\ x=(5)/(4)}`