The lager value of y for which (y-1)²=4y-7 is

the lager value of y is 4.

Step-by-step explanation:

Given;

(y-1)² = 4y - 7

Simplify as follows;

(y - 1)(y - 1) =  4y - 7

y² - y - y + 1 =  4y - 7

y² - 2y  +  1  =  4y - 7

Collect like terms

y² -2y - 4y + 1 + 7 = 0

y² - 6y + 8 = 0

Factorize the equation;

y² -2y - 4y + 8 = 0

y(y - 2) -4(y - 2) = 0

(y - 2)(y - 4) = 0

y = 2   or   y = 4

Thus, the lager value of y is 4.