-step explanation:HLO MATE here's your answer phew!!that is a tough questionlets analyse what we have.we have an equation that saysblah + blah+ blah+ blah = 0, BTW that is rude.we have to find something + 16ohkif one notice carefully then there are two WAYS to solve this question1) ask your teacher or someone who is good at maths2) solve the equationhow to solve the equationall the blah's in the equation are square of some numbersall the squares are positive except zeroyeah zero is neither positive nor negative it is a non negative and non positive number.so the equation isR.H.S.>=0BUT RHS IS ZEROObut how come some positive number give result zero on additionwaittherefore all the blahs need to be zerowe havex=1y=3z=5t=7partyyyyyy.xyzt + 16 = 121Solution below:(x-1) ^2 + (y-3) ^2 + (z-5) ^2 + (t-7) ^2 = 0assuming:x, y, z, t ∈ Rthis can be re-written in the form:a^2 + b^2 + c^2 + d^2 = 0where,a = (x-1)b = (y-3)c = (z-5)d = (t-7)for real numbers,a^2 >= 0b^2 >= 0c^2 >= 0d^2 >= 0In other words,each of a^2, b^2, c^2 and d^2 can never achieve a negative value for it to satisfy the OVERALL equationi.e. LHS ∈ [0, ∞)For equation to achieve a state of LHS = 0,each a^2, b^2, c^2 and d^2 have to be 0Therefore,a = 0 ⇒ x - 1 = 0 ⇒ x = 1b = 0 ⇒ y - 3 = 0 ⇒ y = 3c = 0 ⇒ z - 5 = 0 ⇒ z = 5d = 0 ⇒ t - 7 = 0 ⇒ t = 7Hence,xyzt + 16 = 121I hope its help you mark as brainlist plz