In f (a) = a² – 2ax + y can be factorised as (a – x) (a – y) then find the value of f (4) where x and y are positive real numbers.

<p><span lang="EN-IN">f (a) = a² – 2ax + y</span></p><p><span lang="EN-IN">f (x) = x² – 2x² + y = 0</span></p><p><span lang="EN-IN">– x² + y =0 </span></p><p><span lang="EN-IN">y = x²&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ………. (1)</span></p><p><span lang="EN-IN">f (y) = y² – 2xy + y = 0</span></p><p><span lang="EN-IN">y² – 2xy + x² = 0</span></p><p><span lang="EN-IN">&nbsp; (y – x)² = 0 </span></p><p><span lang="EN-IN">y – x = 0</span></p><p><span lang="EN-IN">y = x</span></p><p><span lang="EN-IN">Put value of y in equation 1 </span></p><p><span lang="EN-IN">We get </span></p><p><span lang="EN-IN">x = y = 1</span></p><p><span lang="EN-IN">So, f (4) = 4² – 2 (4*1) + 1</span></p><p><span lang="EN-IN">= 16 – 8 +1</span></p><p><span lang="EN-IN">= 9</span></p>

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